Related papers: Free transmission problems
This brief note addresses the free boundary problem arising from the steady two-dimensional seepage flow through a rectangular dam. The flow problem consists in finding the free boundary location, and the velocity and pressure fields. The…
We present a variational framework for studying the existence and regularity of solutions to elliptic free boundary problems that do not necessarily minimize energy. As applications, we obtain mountain pass solutions of critical and…
This paper describes a technique to determine the linear well-posedness of a general class of vector elliptic problems that include a steady interface, to be determined as part of the problem, that separates two subdomains. The interface…
In this paper we analyse a boundary value problem for the Laplace equation with a nonlinear non-autonomous transmission conditions on the boundary of a small inclusion of size $\epsilon$. We show that the problem has solutions for…
We consider a transmission problem on a polygonal partition for the two-dimensional conductivity equation. For suitable classes of partitions we establish the exact behaviour of the gradient of solutions in a neighbourhood of the vertexes…
We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. In previous papers, we have established well-posedness of this problem and…
The aim of this note is to review some recent developments on the regularity theory for the stationary and parabolic obstacle problems. After a general overview, we present some recent results on the structure of singular free boundary…
We develop the regularity theory of viscosity solutions to transmission problems for fully nonlinear second order uniformly elliptic equations. Our results give a complete theory of existence, uniqueness, comparison principle, and…
The interface problem for the linear Schr\"odinger equation in one-dimensional piecewise homogeneous domains is examined by providing an explicit solution in each domain. The location of the interfaces is known and the continuity of the…
Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of…
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…
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…
Two boundary value problems for an elliptic equation in divergence form with bounded discontinuous coefficient are studied in a bidomain. On the interface, generalized dynamic boundary conditions such as of the Wentzell-type and…
In this survey we go through some of the recent results about the regularity of vectorial free boundary problems of Bernoulli type and free boundary systems. The aim is to illustrate the general methodologies as well as to outline a…
A class of diffusion driven Free Boundary Problems is considered which is characterized by the initial onset of a phase and by an explicit kinematic condition for the evolution of the free boundary. By a domain fixing change of variables it…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…
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 develop an existence and regularity theory for a class of degenerate one-phase free boundary problems. In this way we unify the basic theories in free boundary problems like the classical one-phase problem, the obstacle problem, or more…
We consider the transmission problem for the Laplace equation on an infinite three-dimensional wedge, determining the complex parameters for which the problem is well-posed, and characterizing the infinite multiplicity nature of the…
We study a class of free boundary problems of ecological models with nonlocal and local diffusions, which are natural extensions of free boundary problems of reaction diffusion systems in there local diffusions are used to describe the…