Related papers: (Non)local and (non)linear free boundary problems
We investigate existence and regularity properties of one-phase free boundary graphs, in connection with the question of whether there exists a complete non-planar free boundary graph in high dimensions.
We give a unified statement and proof of a class of wellknown mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on…
The expression of the free energy of a liquid in terms of an explicit decomposition of the particle configurations into local coordination clusters is examined. We argue that the major contribution to the entropy associated with structural…
A free boundary problem arising from materials science is studied in one-dimensional case. The problem studied here is an obstacle problem for the non-convex energy consisting of a bending energy, tension and an adhesion energy. If the…
We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting free boundary problems may be formulated as Stefan-type…
Integrability and supersymmetry of the supersymmetric extension of the sine-Gordon theory on a half-line are examined and the boundary potential which preserves both the integrability and supersymmetry on the bulk is derived. It appears…
In this paper, we consider a free boundary problem of a semilinear nonhomogeneous elliptic equation with Bernoulli's type free boundary. The existence and regularity of the solution to the free boundary problem are established by use of the…
We consider an elliptic problem with nonlinear boundary condition involving nonlinearity with superlinear and subcritical growth at infinity and a bifurcation parameter as a factor. We use re-scaling method, degree theory and continuation…
We prove that bounded solutions to an overdetermined fully nonlinear free boundary problem in the plane are one dimensional. Our proof relies on maximum principle techniques and convexity arguments.
In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDEs. When the system is open, there are several mechanisms to couple the system with the…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
We study a general class of elliptic free boundary problems equipped with a Dirichlet boundary condition. Our primary result establishes an optimal $C^{1,1}$-regularity estimate for $L^p$-strong solutions at points where the free and fixed…
We consider an elliptic-parabolic free boundary problem that models the fluid flow through a partially saturated porous medium. The free boundary arises as the interface separating the saturated and unsaturated regions. Our main goal is to…
The thesis studies linear and semilinear Dirichlet problems driven by different fractional Laplacians. The boundary data can be smooth functions or also Radon measures. The goal is to classify the solutions which have a singularity on the…
We introduce two different ways of coupling local and nonlocal equations with Neumann boundary conditions in such a way that the resulting model is naturally associated with an energy functional. For these two models we prove that there is…
We investigate singularly perturbed elliptic problems with multiplicative nonlocal diffusion terms subject to Robin boundary conditions. The diffusion depends on a global quantity of the solution, which introduces a nonlocal coupling…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
We study boundary regularity of maps from two-dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which, at the boundary, enter perpendicularly into a support…
We consider Anzellotti-type almost minimizers for the thin obstacle (or Signorini) problem with zero thin obstacle and establish their $C^{1,\beta}$ regularity on the either side of the thin manifold, the optimal growth away from the free…
We summarize the original formulation of the free energy principle, and highlight some technical issues. We discuss how these issues affect related results involving generalised coordinates and, where appropriate, mention consequences for…