Related papers: Free transmission problems
We examine a free transmission problem driven by fully nonlinear elliptic operators. Since the transmission interface is determined endogeneously, our analysis is two-fold: we study the regularity of the solutions and some geometric…
Modelling diffusion processes in heterogeneous media requires addressing inherent discontinuities across interfaces, where specific conditions are to be met. These challenges fall under the purview of Mathematical Analysis as…
We study degenerate fully nonlinear free transmission problems, where the degeneracy rate varies in the domain. We prove optimal pointwise regularity depending on the degeneracy rate. Our arguments consist of perturbation methods, relating…
We study an equation governed by a discontinuous fully nonlinear operator. Such discontinuities are solution-dependent, which introduces a free boundary. Working under natural assumptions, we prove the existence of $L^p$-viscosity and…
We study a fully nonlinear free transmission problem in the presence of general degeneracy laws. Under minimal conditions on the degeneracy of the model, we establish the differentiability of viscosity solutions.
We prove existence and regularity results for free transmission problems governed by fully nonlinear elliptic equations with nonhomogeneous degeneracies.
We study the transmission problem in bounded domains with dissipative boundary conditions. Under some natural assumptions, we prove uniform bounds of the corresponding resolvents on the real axis at high frequency, and as a consequence, we…
We consider a transmission problem consisting of a semilinear parabolic equation in a general non-smooth setting with emphasis on rough interfaces which bear a fractal-like geometry and nonlinear dynamic (possibly, nonlocal)\ boundary…
We examine boundary regularity for a fully nonlinear free transmission problem. We argue using approximation methods, comparing the operators driving the problem with a limiting profile. Working natural conditions on the data of the…
In this paper, we mainly introduce a general method to study the existence and uniqueness of solution of free boundary problems with partially degenerate diffusion.
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…
Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfaces or boundaries. These problems appear in Physics, Probability, Biology, Finance, or Industry, and the study of solutions and free boundaries…
We study a free transmission problem driven by degenerate fully nonlinear operators. Our first result concerns the existence of solutions to the associated Dirichlet problem. By framing the equation in the context of viscosity inequalities,…
We formulate and study a variational two-phase free boundary problem with Robin condition on the interface between the two phases, and we prove existence and regularity of solutions in dimension two
We propose finite difference methods for degenerate fully nonlinear elliptic equations and prove the convergence of the schemes. Our focus is on the pure equation and a related free boundary problem of transmission type. The cornerstone of…
We study regularity properties of the free boundary for solutions of the porous medium equation with the presence of drift. We show the $C^{1,\alpha}$ regularity of the free boundary, when the solution is directionally monotone in space…
We study a two-phase parabolic free boundary problem motivated by the jump of conductivity in composite materials that undergo a phase transition. Each phase is governed by a heat equation with distinct thermal conductivity, and a…
We report on recent progress in the study of evolution processes involving degenerate parabolic equations what may exhibit free boundaries. The equations we have selected follow to recent trends in diffusion theory: considering anomalous…
A mutualist model with nonlocal diffusions and a free boundary is first considered. We prove that this problem has a unique solution defined $t\ge0$, and its dynamics are governed by a spreading-vanishing dichotomy. Some criteria for…
We prove existence and regularity of solutions to degenerate and singular elliptic free boundary problems, where the volume of the positivity set of the solution is prescribed.