Schauder Estimates and Complete Regularity of the Solutions of an Elliptic System

D. V. Portnyagin

Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine

Abstract: We study the complete regularity of the solutions of a nondiagonal elliptic system of nonlinear differential equations of divergent form whose coefficients are sufficiently slowly varying functions of their arguments and whose off-diagonal terms are sufficiently small. To this end, we apply a technique based on successive approximations to the solution and the use of Schauder estimates at each step.

Keywords: nonlinear differential equation, elliptic system, Schauder estimate, complete regularity of solutions, Dirichlet boundary condition, Hölder continuity.

UDC: 517.956.2

Received: 16.08.2007
Revised: 01.03.2008

DOI: 10.4213/mzm4003

 English version: Mathematical Notes, 2009, 85:1, 82–89

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