Related papers: Tangential contact between free and fixed boundari…
In this article we study functionals of the following type $$ \int_{\Omega} \Big ( \langle A(x,u)\nabla u, \nabla u\rangle + \Lambda (x,u) \Big )\,dx $$ here $A(x,u)= A_+(x)\chi_{\{u>0\}}+A_-(x) \chi _{\{u\leq 0\}}$ for some elliptic and…
The main result of this paper concerns the behavior of a free boundary arising from a minimization problem, close to the fixed boundary in two dimensions.
The aim of this paper is to study a free boundary problem for a uniformly elliptic fully non-linear operator. Under certain assumptions we show that free and fixed boundaries meet tangentially at contact points.
In this paper we study regularity properties of the free boundary problem from superconductivity close to a fixed boundary. If the origin is a free boundary point, then we show that the free boundary touches the fixed boundary tangentially.
In the study of classical obstacle problems, it is well known that in many configurations the free boundary intersects the fixed boundary tangentially. The arguments involved in producing results of this type rely on the linear structure of…
In this paper we consider a large class of Bernoulli-type free boundary problems with mixed periodic-Dirichlet boundary conditions. We show that solutions with non-flat profile can be found variationally as global minimizers of the…
For the fully nonlinear Alt-Phillips problem with parameter $\gamma\in(1,2)$, we show that the free boundary intersects the fixed boundary tangentially where the Dirichlet data vanish. For this range of $\gamma$, this result is new even…
In this paper we consider the following two-phase obstacle-problem-like equation in the unit half-ball $\Delta u = \lambda_{+}\chi_{\{u>0\}}-\lambda_{-}\chi_{\{u<0\}}, \lambda_\pm>0$. We prove that the free boundary touches the fixed one in…
This paper is concerned with the study of the behavior of the free boundary for a class of solutions to a one-phase Bernoulli free boundary problem with mixed periodic-Dirichlet boundary conditions. It is shown that if the free boundary of…
In this paper, we propose an efficient numerical treatment for solving contact problems with friction between deformable bodies. The discretized normal and tangential constraints at the candidate contact interface are expressed by using…
In this paper we consider a weakly coupled $p$-Laplacian system of a Bernoulli type free boundary problem, through minimization of a corresponding functional. We prove various properties of any local minimizer and the corresponding free…
We study the regularity of the interface for a new free boundary problem introduced by Caffarelli and Kriventsov. We show that for minimizers of the functional \[ F_1(A,u) = \int_A |\nabla u|^2 d\mathcal{L}^n + \int_{\partial A} u^2 +…
We discuss the extent to which solutions to one-phase free boundary problems can be characterized according to their topological complexity. Our questions are motivated by fundamental work of Luis Caffarelli on free boundaries and by…
We prove new boundary regularity results for minimizers to the one-phase Alt-Caffarelli functional (also known as Bernoulli free boundary problem) in the case of continuous and H\"older-continuous boundary data. As an application, we use…
Existence and regularity of minimizers for a geometric variational problem is shown. The variational integral models an energy contribution of the interface between two immiscible fluids in the presence of surfactants and includes a…
We study higher critical points of the variational functional associated with a free boundary problem related to plasma confinement. Existence and regularity of minimizers in elliptic free boundary problems have already been studied…
In this paper we study the local behavior of solutions to some free boundary problems. We relate the theory of quasi-conformal maps to the regularity of the solutions to nonlinear thin-obstacle problems; we prove that the contact set is…
In the present paper we show that the normal contact problem between two elastic bodies in the halfspace approximation can always be transformed to an equivalent problem of the indentation of a profile into an elastic Winkler foundation.…
We provide evidence for the existence of non-trivial unitary conformal boundary conditions for a three-dimensional free scalar field, which can be obtained via a coupling to the m'th unitary diagonal minimal model. For large m we can…
We start the investigation of free boundary variational models featuring varying singularities. The theory depends strongly on the nature of the singular power $\gamma(x)$ and how it changes. Under a mild continuity assumption on…