Related papers: Approximation of partial differential equations on…
This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective in a well-chosen subset of arbitrarily small measure.
We consider a linear partial integro-differential equation that arises in the modeling of various physical and biological processes. We study the problem in a spatial periodic domain. We analyze numerical stability and numerical convergence…
For a wide class of polynomially nonlinear systems of partial differential equations we suggest an algorithmic approach to the s(trong)-consistency analysis of their finite difference approximations on Cartesian grids. First we apply the…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
The goal of this paper is to generalize the main results of [KM] and subsequent papers on metric Diophantine approximation with dependent quantities to the set-up of systems of linear forms. In particular, we establish `joint strong…
We study existence and uniqueness of bounded solutions to a fractional sublinear elliptic equation with a variable coefficient, in the whole space. Existence is investigated in connection to a certain fractional linear equation, whereas the…
This paper presents a finite-dimensional approximation for a class of partial differential equations on the space of probability measures. These equations are satisfied in the sense of viscosity solutions. The main result states the…
In this work, we present a systematic approach to investigate the existence, multiplicity, and local gradient regularity of solutions for nonlocal quasilinear equations with local gradient degeneracy. Our method involves an interactive…
We study conformal harmonic coordinates on Riemannian manifolds. These are coordinates constructed as quotients of solutions to the conformal Laplace equation. We show their existence under general conditions. We find that conformal…
We consider a mixed dimensional elliptic partial differential equation posed in a bulk domain with a large number of embedded interfaces. In particular, we study well-posedness of the problem and regularity of the solution. We also propose…
We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in two steps: we first show some uniform energy estimates and…
In this paper we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation of such problems, including their well-posedness and…
In this paper, we establish $L_p$ estimates and solvability for time fractional divergence form parabolic equations in the whole space when leading coefficients are merely measurable in one spatial variable and locally have small mean…
For a homogenization problem associated to a linear elliptic operator, we prove the existence of a distributional corrector and we find an approximation scheme for the homogenized coefficients. We also study the convergence rates in the…
A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic…
In this article, we summarize the results on symmetric conformal geometries. We review the results following from the general theory of symmetric parabolic geometries and prove several new results for symmetric conformal geometries. In…
We consider the problem of establishing dense correspondences within a set of related shapes of strongly varying geometry. For such input, traditional shape matching approaches often produce unsatisfactory results. We propose an ensemble…
The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…