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Advances in Nonlinear Analysis

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A-priori bounds and existence for solutions of weighted elliptic equations with a convection term

Ky Ho / Inbo SimORCID iD: http://orcid.org/0000-0002-1618-054X
Published Online: 2016-04-07 | DOI: https://doi.org/10.1515/anona-2015-0177


We investigate weighted elliptic equations containing a convection term with variable exponents that are subject to Dirichlet or Neumann boundary condition. By employing the De Giorgi iteration and a localization method, we give a-priori bounds for solutions to these problems. The existence of solutions is also established using Brezis’ theorem for pseudomonotone operators.

Keywords: weighted variable exponent Lebesgue–Sobolev spaces; a-priori bound; De Giorgi iteration; localization method; pseudomonotone operators

MSC 2010: 35J20; 35J60; 35J70; 47J10; 46E35


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About the article

Received: 2015-12-22

Revised: 2016-03-03

Accepted: 2016-03-04

Published Online: 2016-04-07

Published in Print: 2017-11-01

The first author was supported by the project LO1506 of the Czech Ministry of Education, Youth and Sports. The second author was supported by the National Research Foundation of Korea Grant funded by the Korea Government (MEST) (NRF-2015R1D1A3A01019789).

Citation Information: Advances in Nonlinear Analysis, Volume 6, Issue 4, Pages 427–445, ISSN (Online) 2191-950X, ISSN (Print) 2191-9496, DOI: https://doi.org/10.1515/anona-2015-0177.

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