Regularity of Weak Solutions to Nondiagonal Elliptic Systems with Composite Boundary Conditions

A. A. Arkhipova, G. V. Grishina

Research output

Abstract

We consider a model problem in a half-ball for linear and quasilinear elliptic systems of equations with nondiagonal principal matrix. It is assumed that the components of the solution are interconnected by Dirichlet and Neumann type boundary conditions through some matrix on the planar boundary of the half-ball. We establish the Hölder continuity of weak solutions to linear systems and the partial regularity of weak solutions to quasilinear systems. To treat such composite boundary conditions, we apply a modification of the method of A-harmonic approximations adapted to problems under consideration.

Original languageEnglish
Pages (from-to)791-819
Number of pages29
JournalJournal of Mathematical Sciences (United States)
Volume247
Issue number6
DOIs
Publication statusPublished - 1 Jun 2020

Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Regularity of Weak Solutions to Nondiagonal Elliptic Systems with Composite Boundary Conditions'. Together they form a unique fingerprint.

Cite this