An alternative approach to the Hölder continuity of solutions to some elliptic equations

Duzgun, Fatma Gamze;Marcellini, Paolo;Vespri, Vincenzo

2014-01-01

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Abstract

We give an alternative and self contained proof of the Holder continuity of locally bounded solutions to some elliptic equations, including the equation associated with the p-Laplacian operator. We combine the techniques introduced by De Giorgi and Moser with a 1-dimensional Poincare inequality. (C) 2013 Elsevier Ltd. All rights reserved.