Conditions for the solvability of boundary value problems for quasi-elliptic systems in a half-space
type: Item
instance of: scholarly article
title: Conditions for the solvability of boundary value problems for quasi-elliptic systems in a half-space
zbMATH Open document ID: 1255.35102
DOI: 10.1134/S0012266112030056
published in: Differential Equations
publication date: 2012-08-13T00:00:00Z
review text: The author considers boundary value problems in \(\mathbb R^n_+=\{x=(x',x_n)\;:\;x'\in\mathbb R^{n-1},\;x_n>0\}\) for quasi-elliptic systems of the form \[ \mathcal L(D_x)U=F(x),\quad x\in\mathbb R^n_+,\qquad \mathcal B(D_x)U|_{x_n=0}=0.\tag{1} \] Conditions, imposed on the matrix differential operator \(\mathcal L(D_x)\), define it as a quasi-elliptic operator introduced by \textit{L. R. Volevich} [Mat. Sb., N. Ser. 59(101), Suppl., 3--52 (1962; Zbl 0161.07801)], and conditions, imposed on the matrix differential operator \(\mathcal B(D_x)\), make the problem (1) satisfying the Lopatinskii condition. The author obtains necessary and sufficient conditions for unique solvability of the problem in appropriate Sobolev spaces.
reviewed by: Yakov Yakubov
Mathematics Subject Classification ID: 35J58
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 6065260
zbMATH Keywords: quasi-elliptic system
zbMATH Keywords: Lopatinskii condition
zbMATH Keywords: Sobolev space
zbMATH Keywords: unique solvability
author: L. N. Bondar'
MaRDI profile type: Publication
cites work: Q5545709
cites work: MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS WITH A DISCONTINUOUS NONLINEARITY
cites work: Multidimensional functional equations and normalization of local matrix- functions
cites work: Solvability conditions of boundary value problems for quasielliptic systems
cites work: Q3545564
cites work: Q3733978
cites work: Q3704256
description: scientific article; zbMATH DE number 6065260