Related papers: Interior transmission problems with coefficients o…
We establish interior Lipschitz estimates at the macroscopic scale for solutions to systems of linear elasticity with rapidly oscillating periodic coefficients and mixed boundary conditions in domains periodically perforated at a…
This paper is concerned with the intrinsic geometric structures of conductive transmission eigenfunctions. The geometric properties of interior transmission eigenfunctions were first studied in [9]. It is shown in two scenarios that the…
We obtain the regularity of solutions in Sobolev spaces for the mixed Dirichlet-conormal problem for parabolic operators in cylindrical domains with time-dependent separations, which is the first of its kind. Assuming the boundary of the…
The spectrum of interior transmission problem is the zero set of certain entire functional determinant. It is classic that we deploy the series of exponential polynomials to approximate the distribution of the roots of the entire functions…
In this work, we study the eigenvalue problem associated with the bidomain operator in an anisotropic heterogeneous domain composed of three subregions representing the left ventricle, the septum, and the right ventricle. The anisotropic…
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 for the Helmholtz equation across the boundary of an extension domain. A such boundary can be Lipschitz, fractal, or of varying Hausdorff dimension for instance. We generalise the notions of layer…
A novel variational formulation of layer potentials and boundary integral operators generalizes their classical construction by Green's functions, which are not explicitly available for Helmholtz problems with variable coefficients.…
In this paper following the same methods in [M. Kadakal, O. Sh. Mukhtarov, Sturm-Liouville problems with discontinuities at two points, Comput. Math. Appl., 54 (2007) 1367-1379] we investigate discontinuous two-point boundary value problems…
We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The…
In this note we review some recent results concerning integral representation properties of local functionals driven by Lipschitz continuous anisotropies.
In this paper, we consider a new transmission eigenvalue problem derived from the scattering by a clamped cavity in a thin elastic material. Scattering in a thin elastic material can be modeled by the Kirchhoff--Love infinite plate problem.…
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 paper we are concerned with a new class of BVP' s consisting of eigendependent boundary conditions and two supplementary transmission conditions at one interior point. By modifying some techniques of classical Sturm-Liouville theory…
We prove regularity results such as interior Lipschitz regularity and boundary continuity for the Cauchy-Dirichlet problem associated to a class of parabolic equations inspired by the evolutionary $p$-Laplacian, but extending it at a wide…
In this study we are concerned with a class of generalized BVP' s consisting of eigendependent boundary conditions and supplementary transmission conditions at finite number interior points. By modifying some techniques of classical…
Consider the interior transmission problem arising in inverse boundary value problems for the diffusion equation with discontinuous diffusion coefficients. We prove the unique solvability of the interior transmission problem by constructing…
We prove existence and regularity results for free transmission problems governed by fully nonlinear elliptic equations with nonhomogeneous degeneracies.
In this paper, we consider a free boundary problem with volume constraint. We show that positive minimizer is locally Lipschitz and the free boundary is analytic away from a singular set with Hausdorff dimension at most $n-8$.
We study a weighted eigenvalue problem with anisotropic diffusion in bounded Lipschitz domains $\Omega\subset \mathbb{R}^{N} $, $N\ge1$, under Robin boundary conditions, proving the existence of two positive eigenvalues $\lambda^{\pm}$…