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Matematicheskie Zametki, 2009, Volume 85, Issue 1, Pages 89–97
DOI: https://doi.org/10.4213/mzm4003 (Mi mzm4003) 		 
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
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DOI: https://doi.org/10.4213/mzm4003
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.
Received: 16.08.2007
Revised: 01.03.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 1, Pages 82–89
DOI: https://doi.org/10.1134/S0001434609010088
Bibliographic databases:
UDC: 517.956.2
Language: Russian
Citation: D. V. Portnyagin, “Schauder Estimates and Complete Regularity of the Solutions of an Elliptic System”, Mat. Zametki, 85:1 (2009), 89–97; Math. Notes, 85:1 (2009), 82–89
Citation in format AMSBIB
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