相关论文: Tangential Touch between the Free and the Fixed Bo…

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 this paper, we show that given appropriate boundary data, the free boundary and the fixed boundary of minimizers of functionals of type \eqref{functional} contact each other in a tangential fashion. We prove this result via…

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 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…

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 studies local properties of a two phase free boundary problem for the fractional Laplacian. The main result states that the two free boundaries of the positive and negativity sets cannot touch.

In this paper, we study superlinear systems that give rise to free boundaries. Such systems appear for example from the minimization of the energy functional $$ \int_{\Omega}\left(|\nabla\mathbf{u}|^2+\frac2p|\mathbf{u}|^p\right),\quad…

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…

We consider the behavior of the nonlocal minimal surfaces in the vicinity of the boundary. By a series of detailed examples, we show that nonlocal minimal surfaces may stick at the boundary of the domain, even when the domain is smooth and…

We study a class of semilinear free boundary problems in which admissible functions $u$ have a topological constraint, or spanning condition, on their 1-level set. This constraint forces $\{u=1\}$, which is the free boundary, to behave like…

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…

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…

We study a linear problem that arises in the study of dynamic boundaries, in particular in free boundary problems in connection with fluid dynamics. The equations are also very natural and of interest on their own.

The problem of the exact bounded control of oscillations of the two-dimensional wave equation is considered. Control force is applied to the boundary of the membrane, which is located in a domain on a plane. The goal of the control is to…

We study the free boundary Euler equations in two spatial dimensions. We prove that if the boundary is sufficiently regular, then solutions of the free boundary fluid motion converge to solutions of the Euler equations in a fixed domain…

A horizontal $N$-dimensional plane, having a diffusion of its own, exchanges with the lower half space. There, a reaction-diffusion process, modelled by a free boundary problem, takes place. We wish to understand whether, and how, the free…

We consider the free boundary problem arising from an energy functional which is the sum of a Dirichlet energy and a nonlinear function of either the classical or the fractional perimeter. The main difference with the existing literature is…

In this paper we give an overview of some recent and older results concerning free boundary problems governed by elliptic operators.

We study a free transmission problem in which solution minimizes a functional with different definitions in positive and negative phase of function. We prove some asymptotic regularity results when the jumps of the diffusion coefficients…