Related papers: On jump relations of anisotropic elliptic interfac…
The effective anisotropic stresses induced by the scalar modes of the geometry depend on the coordinate system so that the comparison of the competing results is ultimately determined by the evolution of the pivotal variables in each…
In this article we introduce a procedure, which allows to recover the potentially very good approximation properties of tensor-based model reduction procedures for the solution of partial differential equations in the presence of interfaces…
We derive a correct first-order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted. Most previous perturbative methods give incorrect results for this case,…
An intrinsic feature of nearly all internal interfaces in crystalline systems (homo- and hetero-phase) is the presence of disconnections (topological line defects constrained to the interface that have both step and dislocation character).…
We discuss the theoretical solution to the differential equations governing accelerating edge dislocations in anisotropic crystals. This is an important prerequisite to understanding high speed dislocation motion, including an open question…
In this paper, we prove sharp estimates and existence results for anisotropic nonlinear elliptic problems with lower order terms depending on the gradient. Our prototype is: $ \left\{ \begin{array}{ll} -\mathcal Q_{p}u =[H(Du)]^{q}+f(x)…
In this paper, we propose an extended mixed finite element method for elliptic interface problems. By adding some stabilization terms, we present a mixed approximation form based on Brezzi-Douglas-Marini element space and the piecewise…
In this paper we study a nonlocal critical growth elliptic problem driven by the fractional Laplacian in presence of jumping nonlinearities. In the main results of the paper we prove the existence of a nontrivial solution for the problem…
We study the existence and uniqueness for weak solutions to some classes of anisotropic elliptic Dirichlet problems with data belonging to the natural dual space.
We analyze the continuum limit of a thresholding algorithm for motion by mean curvature of one dimensional interfaces in various space-time discrete regimes. The algorithm can be viewed as a time-splitting scheme for the Allen-Cahn equation…
We associate curves of isotropic, Lagrangian and coisotropic subspaces to higher order, one parameter variational problems. Minimality and conjugacy properties of extremals are described in terms of these curves.
The paper is devoted to the study of asymptotic behavior of solutions for nonlocal elliptic problems in weighted spaces. We deal with the most difficult case where the support of nonlocal terms intersects with the boundary of a plane…
We evaluate reflected entropy in certain anisotropic boundary theories dual to nonrelativistic geometries using holography. It is proposed that this quantity is proportional to the minimal area of the entanglement wedge cross section. Using…
Boundary differentiability is shown for solutions of nondivergence elliptic equations with unbounded drift
We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.
We study the ground state of a classical X-Y model with $p \ge 3$-fold spin anisotropy $D$ in a uniform external field, $H$. An interface is introduced into the system by a suitable choice of boundary conditions. For large $D$, as $H \to…
In this paper, the classical JKR theory of the adhesive contact of isotropic elastic spheres is extended to consider the effect of anisotropic elasticity. The contact area will then generally be non-circular, but in many cases it can…
The present paper introduces an efficient and accurate numerical scheme for the solution of a highly anisotropic elliptic equation, the anisotropy direction being given by a variable vector field. This scheme is based on an asymptotic…
Nonequilibrium dynamics at interfaces is generally driven by a chemical potential. Here we demonstrate a generic technique to derive the basic equations of motion, boundary conditions and the chemical potential in a consistent way from…
We consider a coupled system describing the interaction between acoustic and elastic regions, where the coupling occurs not via material properties but through an interaction on an interface separating the two regimes. Evolutionary…