Free boundary problems and related topics

Programme theme

Free boundary problems are today considered as one of the most important directions in the mainstream of the analysis of partial differential equations (PDEs), with an abundance of applications in various sciences and real world problems. In the last two decades, various new ideas, techniques, and methods have been developed, and new important, challenging problems in physics, engineering, industry, finance, biology, and other areas have arisen. The topics of this programme are at the forefront of current exciting developments. We realise that there have been few activities on free boundary problems in recent decades in the UK. We strongly believe that a thematic programme at the Newton Institute will have a huge impact on the development of FBPs from all points of view. The programme is directed towards theory, numerics and applications. It will further enhance the interaction between UK mathematicians and top international researchers in this field and strengthen the UK expertise in FBPs. The study of free boundary problems is an extremely broad topic due to the abundance of applications. This breadth presents challenges and opportunities! Many problems treated by applied scientists and numerical analysts are not well known amongst theoretical people, and vice versa. This leads to the development of the topic in different directions and sometimes with no links. However, often there are several unifying themes with respect to methodologies and techniques. The aim of programme is to enhance those links and unifying techniques by bringing together the relevant specialists. PROGRAMME PUBLICATIONS Preprints: The Newton Institute has its own Preprint Series (http://www.newton.ac.uk/preprints). Free Boundary Problems and Related Topics visitors are encouraged to submit relevant papers to the series (http://www.newton.ac.uk/event/frb/preprints). All papers must have been either completed at the Institute or based on work that took place partially or wholly at the Institute. You can still submit material to the preprint series even after your visit has ended as long as it is based on work that you did during your visit. Journal articles: A special theme issue of Philosophical Transactions A was published in Septermber 2015 containing output from this programme. A special issue of the EMS journal Interfaces and Free Boundaries contains output from this programme.

The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:

The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Free boundary problems and related topics, where work on this paper was undertaken. This work was supported by EPSRC grant EP/K032208/1.

Click here to download the programme's final scientific report

Preprints

Title	Year	Programme	Publication Date
Infinitely many solutions for a class of sublinear Schrödinger equations with indefinite potentials Authors: A Bahrouni, H Ounaies, Vicentiu Radulescu Download PDF	2013	FRB	21 October 2016
Equilibrium problems techniques in the qualitative analysis of quasi-hemivariational inequalities Authors: B Alleche, Vicentiu Radulescu Download PDF	2013	FRB	21 October 2016
On the regularity of the free boundary for quasilinear obstacle problems Authors: S Challal, A Lyaghfouri, JF Rodrigues, R Teymurazyan Download PDF	2013	FRB	21 October 2016
Nonlocal $\it p$-laplace equations depending on the $\it L^p$ norm of the gradient Authors: Michel Chipot, T Savitska Download PDF	2013	FRB	21 October 2016
Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity Authors: Giuseppe Buttazzo, Michiel van den Berg, B Velichkov Download PDF	2013	FRB	21 October 2016
On regularity properties of solutions to hysteresis-type problems Authors: D E Apushkinskaya, N N Uraltseva Download PDF	2013	FRB	21 October 2016
Hopf's lemma for a class of singular/degenerate PDE-s Authors: Hayk Mikayelyan, H Shaghholian Download PDF	2013	FRB	21 October 2016
Transformations of self-similar solutions for porous medium equations of fractional type Authors: Diana Stan, F Del Teso, Juan Luis Vázquez Download PDF	2013	FRB	21 October 2016
Fast and accurate finite element approximation of wave maps into spheres Authors: Soeren Bartels Download PDF	2013	FRB	21 October 2016
Isoperimetric inequalities for the principal eigenvalue of a membrane and the energy of problems with Robin boundary conditions Authors: Catherine Bandle, Alfred Wagner Download PDF	2013	FRB	21 October 2016
The mesa problem for the fractional porous medium equation Authors: Juan Luis Vázquez Download PDF	2013	FRB	21 October 2016
On the mathematical analysis of thick fluids Authors: JF Rodrigues Download PDF	2013	FRB	21 October 2016
Error analysis for an ALE evolving surface finite element method Authors: CM Elliott, Mirna Golubic Venkataraman Download PDF	2013	FRB	21 October 2016
An abstract framework for parabolic PDEs on evolving spaces Authors: A Alphonse, CM Elliott, B Stinner Download PDF	2013	FRB	21 October 2016
The saddle-point formulation and finite element method for the Stefan problem with surface tension Authors: CB Davis, Shawn Walker Download PDF	2013	FRB	21 October 2016
A simple scheme for the approximation of elastic vibrations of inextensible curves Authors: Soeren Bartels Download PDF	2013	FRB	21 October 2016
Analysis of a variational model for nematic shells Authors: Antonio Segatti, M Snarski, M Veneroni Download PDF	2013	FRB	21 October 2016
On a Cahn-Hilliard type phase field system related to tumor growth Authors: Pierluigi Colli, G Gilardi, D Hilhorst Download PDF	2013	FRB	21 October 2016
More on the potential for the farthest-point distance function Authors: Bernd Kawohl, C Nitsch, G Sweers Download PDF	2013	FRB	21 October 2016
Distributed and boundary control problems for the semidiscrete Cahn-Hilliard/Navier-Stokes system with nonsmooth Ginzburg-Landau energies Authors: Michael Hintermüller, D Wegner Download PDF	2013	FRB	21 October 2016
The Tikhonov regularization for equilibrium problems and applications to quasi-hemivariational inequalities Authors: B Alleche, Vicentiu Radulescu, M Sebaoui Download PDF	2013	FRB	21 October 2016
Nondegeneracy in the obstacle problem with a degenerate force term Authors: K Yeressian Download PDF	2013	FRB	21 October 2016
Two Robin boundary value problems with opposite sign Authors: Catherine Bandle, Alfred Wagner Download PDF	2013	FRB	21 October 2016
On generalized solutions of axisymmetric two-phase incompressible viscous flow with surface tension Authors: K Yeressian Download PDF	2013	FRB	21 October 2016
Competition phenomena for difference equations with oscillatory nonlinearities Authors: M Malin, Vicentiu Radulescu Download PDF	2013	FRB	21 October 2016
Global bifurcation of steady gravity water waves with critical layers Authors: A Constantin, W Strauss, Eugen Varvaruca Download PDF	2013	FRB	21 October 2016
Morse's index formula in VMO for compact manifolds with boundary Authors: G Canevari, Antonio Segatti, M Veneroni Download PDF	2013	FRB	21 October 2016
Time-periodic solutions of advection-diffusion equations on moving hypersurfaces Authors: CM Elliott, Hans Fritz Download PDF	2013	FRB	21 October 2016
A computational approach to an optimal partition problem on surfaces Authors: CM Elliott, Tom Ranner Download PDF	2013	FRB	21 October 2016
Vanishing viscosity solutions of the compressible Euler equations with spherical symmetry and large initial data Authors: GG Chen, M Perepelitsa Download PDF	2013	FRB	21 October 2016
Obstacle problem with a degenerative force term Authors: K Yeressian Download PDF	2013	FRB	21 October 2016
Regularity of solutions of the fractional porous medium flow with exponent 1/2 Authors: Luis Caffarelli, Juan Luis Vázquez Download PDF	2013	FRB	21 October 2016
A surgery result for the spectrum of the Dirichlet Laplacian Authors: Dorin Bucur, D Mazzoleni Download PDF	2013	FRB	21 October 2016
Free boundary problems in shock reflection/diffraction and related transonic flow problems Authors: GG Chen, Mikhail Feldman Download PDF	2013	FRB	21 October 2016
A new isoperimetric inequality for the elasticae Authors: Dorin Bucur, Antoine Henrot Download PDF	2013	FRB	21 October 2016
A nonlocal diffusion problem on manifolds Authors: Catherine Bandle, MDM Gonzalez, Marco Fontelos, Noemi Wolanski Download PDF	2013	FRB	21 October 2016

Workshops

FRBW01

Introductory school: free boundary problems and related topics

6 January 2014 to 10 January 2014

Satellite

FRBW02

Free Boundaries and Moving Interfaces Workshop

10 February 2014 to 14 February 2014

Satellite

FRBW03

Recent developments and challenges in interface and free boundary problems

25 March 2014 to 28 March 2014

FRBW04

International conference on free boundary problems: theory and applications

23 June 2014 to 27 June 2014

Seminars

Wednesday 15th January 2014
14:00 to 15:00	Optimal potentials for Schrödinger operators	Room 2
15:15 to 16:15	Minimization of Dirichlet eigenvalues	Room 2

Wednesday 22nd January 2014
14:00 to 15:00	Nonlinear eigenvalue problems for nonhomegenous differential operators	Room 2
15:15 to 16:15	Nonlocal problems of p-laplacian type	Room 2

Wednesday 29th January 2014
14:00 to 15:00	Singular Integrals and Geometric Measure Theory: towards a solution of David--Semmes problem.	Room 2
15:15 to 16:15	On the Mathematical Analysis of Thick Fluids	Room 2

Wednesday 5th February 2014
14:00 to 15:00	Energy minimizing maps with free boundaries	Room 2
15:15 to 16:15	Surface PDEs and Interfaces	Room 2

Thursday 6th February 2014
14:00 to 15:45	Free Boundary Problems in Transonic Flow: Introudction I	Room 2
16:00 to 17:00	Free Boundary Problems in Transonic Flow: Introudction II	Room 2

Monday 10th February 2014
13:00 to 14:00	Optimal partitions for first eigenvalue; numerical approximations and related problems	Room 2

Wednesday 12th February 2014
14:00 to 15:00	Flatness implies smoothness for the porous medium equation	Room 2
15:15 to 16:15	On regularity properties of solutions to hysteresis-type problems.	Room 2

Tuesday 18th February 2014
13:00 to 14:00	Computational methods for an optimal partition problem on surfaces	Room 1

Tuesday 25th February 2014
13:00 to 14:30	Shape optimization of spectral functionals: a short introduction.	Room 2

Wednesday 26th February 2014
14:00 to 15:00	Free energies, discrete Hamiltonians and two scale convergence in statistical mechanics.	Room 2
15:15 to 16:15	Multidimensional Shock Waves and Free Boundary Problems	Room 2

Wednesday 5th March 2014
14:00 to 15:00	First and second variation of domain functionals and applications to problems with Robin boundary conditions.	Room 1
15:15 to 16:15	From Boltzmann to Euler: Hilbert's 6th problem revisited.	Room 1

Thursday 6th March 2014
13:00 to 14:00	Nonlinear Fractional Diffusion Equations. Numerics and Free Boundaries	Discussion Room

Tuesday 11th March 2014
13:00 to 14:00	Nondegeneracy of solution to degenerate obstacle problem.	Room 2

Thursday 13th March 2014
14:00 to 15:00	Mathematical Modeling of the Cellular Cytoskeleton.	Room 2
15:15 to 16:15	An overdetermined Free Boundary Problem with non constant boundary conditions	Room 2

Tuesday 18th March 2014
13:00 to 14:00	Regularity of the Mumford-Shah minimizers at the crack-tip	Room 2

Wednesday 19th March 2014
14:00 to 15:00	Contact-point behaviour of the free boundary for the porous-medium equation	Room 2
15:15 to 16:15	Modelling and simulation of cell motility with surface finite elements	Room 2

Wednesday 2nd April 2014
14:00 to 15:00	A nonstandard PDE system of viscous Cahn-Hilliard type related to a model for phase segregation.	Room 2
15:15 to 16:15	The longest shortest fence and the stability of floating trees	Room 2

Tuesday 8th April 2014
13:00 to 14:00	The eigenvalue problem for the infinity Laplacian	Discussion Room

Wednesday 9th April 2014
14:00 to 15:00	Non-univalent solutions of the Polubarinova-Galin equation	Room 1
15:15 to 16:15	Traffic on networks: modeling and analysis	Room 1

Tuesday 15th April 2014
13:00 to 14:00	Interior regularity of solutions to elliptic fully nonlinear free boundary problems.	Discussion Room

Wednesday 16th April 2014
14:00 to 15:00	Shock Reflection, von Neumann conjectures, and free boundary problems	Room 2
15:15 to 16:15	The Signorini problem for the heat equation: regularity of the solution and of the free boundary	Room 2

Thursday 17th April 2014
16:00 to 17:00	informal discussion	Room 1

Wednesday 23rd April 2014
14:00 to 15:00	Phase field modelling of drops in electric fields	Room 2
15:15 to 16:15	Does p matter in the p-obstacle problem?	Room 2

Thursday 24th April 2014
11:00 to 12:30	Numerical Methods for (Quasi)Variational Inequalities - Part I	Room 2
14:30 to 16:00	Numerical Methods for (Quasi)Variational Inequalities - Part II	Room 2

Tuesday 29th April 2014
13:00 to 14:00	Some observations on a fractional Cahn Hilliard equation and its relations with the fractional Porous Medium equation	Discussion Room

Wednesday 30th April 2014
14:00 to 15:00	Free boundary regularity in the parabolic Signorini problem	Room 2
15:15 to 16:15	Nonlinear fractional diffusion equations. Two problems with free boundaries	Room 2

Wednesday 7th May 2014
14:00 to 15:00	Harnack's inequality for the inhomogeneous $p(x)-$laplace equation	Room 2
15:15 to 16:15	The Calderón Problem For Schrödinger Operators	Room 2

Tuesday 13th May 2014
13:00 to 14:00	Time-periodic solutions of advection-diffusion equations on moving hypersurfaces.	Discussion Room
15:00 to 16:30	Why people in hyperbolic conservation laws are interested in free boundary problems.	Room 1

Wednesday 14th May 2014
14:00 to 15:00	Weak singularities in the multi-dimensional Riemann Problem	Room 2
15:15 to 16:15	Interface singularities for the Euler equations.	Room 2

Thursday 15th May 2014
09:00 to 11:00	Informal discussion	Room 2

Tuesday 20th May 2014
15:00 to 16:30	An Introduction to Free Boundary Problems in MHD	Room 2

Thursday 22nd May 2014
11:00 to 12:00	A transportation approach to random matrices.	Room 2
14:00 to 15:00	Confinement in the framework of Schrödinger equations: a revision of the classical "particle in a box" example and further free boundary results.	Room 2
15:15 to 16:15	Stability of the linearized MHD-Maxwell free interface problem	Room 2

Friday 23rd May 2014
10:45 to 12:30	informal discussion	Room 1

Tuesday 27th May 2014
10:00 to 10:55	Propagation and blocking for reaction-diffusion equations in non homogeneous media.	Room 1
10:55 to 11:15	Coffee Break	No Room Required
11:15 to 12:10	Global Bifurcation of Steady Gravity Water Waves with Critical Layers	Room 1
13:30 to 14:25	TBA	Room 1
14:30 to 15:25	Free boundary problems in random environments.	Room 1
15:25 to 16:00	Coffee Break	No Room Required
16:00 to 17:00	What Makes a Surface "Optimal" : Rothschild Distinguished Visiting Fellow Lecture	Room 1

Wednesday 4th June 2014
14:00 to 15:00	Regularity of local minimizers of the interaction energy via obstacle problems.	Room 2

Wednesday 11th June 2014
14:00 to 15:00	Nonlinear elliptic equations with absorption	Room 2
15:15 to 16:15	On incompressible two-phase flows with phase transitions	Room 2

Wednesday 18th June 2014
14:00 to 16:00	Phase transition problems involving minimal surfaces	Room 2

Thursday 19th June 2014
14:00 to 15:00	A classical Perron method for existence of smooth solutions to boundary value & obstacle problems for boundary-degenerate elliptic operators via holomorphic map	Room 1
15:15 to 16:15	Modelling the Growth of Tyndall Stars	Room 1

Wednesday 2nd July 2014
14:00 to 15:00	Interactions of a gasdynamic type. Two significant multidimensional examples of a constructive and classifying approach	Room 2

Free boundary problems and related topics

Organisers

Gui-Qiang G. Chen University of Oxford
Henrik Shahgholian KTH - Royal Institute of Technology
Juan Luis Vázquez Universidad Autonoma de Madrid

Free boundary problems and related topics

Programme theme

Preprints

Infinitely many solutions for a class of sublinear Schrödinger equations with indefinite potentials

Equilibrium problems techniques in the qualitative analysis of quasi-hemivariational inequalities

On the regularity of the free boundary for quasilinear obstacle problems

Nonlocal $\it p$-laplace equations depending on the $\it L^p$ norm of the gradient

Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity

On regularity properties of solutions to hysteresis-type problems

Hopf's lemma for a class of singular/degenerate PDE-s

Transformations of self-similar solutions for porous medium equations of fractional type

Fast and accurate finite element approximation of wave maps into spheres

Isoperimetric inequalities for the principal eigenvalue of a membrane and the energy of problems with Robin boundary conditions

The mesa problem for the fractional porous medium equation

On the mathematical analysis of thick fluids

Error analysis for an ALE evolving surface finite element method

An abstract framework for parabolic PDEs on evolving spaces

The saddle-point formulation and finite element method for the Stefan problem with surface tension

A simple scheme for the approximation of elastic vibrations of inextensible curves

Analysis of a variational model for nematic shells

On a Cahn-Hilliard type phase field system related to tumor growth

More on the potential for the farthest-point distance function

Distributed and boundary control problems for the semidiscrete Cahn-Hilliard/Navier-Stokes system with nonsmooth Ginzburg-Landau energies

The Tikhonov regularization for equilibrium problems and applications to quasi-hemivariational inequalities

Nondegeneracy in the obstacle problem with a degenerate force term

Two Robin boundary value problems with opposite sign

On generalized solutions of axisymmetric two-phase incompressible viscous flow with surface tension

Competition phenomena for difference equations with oscillatory nonlinearities

Global bifurcation of steady gravity water waves with critical layers

Morse's index formula in VMO for compact manifolds with boundary

Time-periodic solutions of advection-diffusion equations on moving hypersurfaces

A computational approach to an optimal partition problem on surfaces

Vanishing viscosity solutions of the compressible Euler equations with spherical symmetry and large initial data

Obstacle problem with a degenerative force term

Regularity of solutions of the fractional porous medium flow with exponent 1/2

A surgery result for the spectrum of the Dirichlet Laplacian

Free boundary problems in shock reflection/diffraction and related transonic flow problems

A new isoperimetric inequality for the elasticae

A nonlocal diffusion problem on manifolds