Moser iteration applied to elliptic equations with critical growth on the boundary

2018/05/03 by Marino, Greta, Winkert, Patrick · 2 citations
#35B45 #35J25 #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.01154

Abstract

This paper deals with boundedness results for weak solutions of an elliptic equation where the functions are Carathéodory functions satisfying certain p-structure conditions that have critical growth even on the boundary. Based on a modified version of the Moser iteration we are able to prove that every weak solution of our problem is bounded up to the boundary. Under some additional assumptions this leads directly to C^1,α-regularity for weak solutions of the problem.

Cited by

• Global boundedness of weak solutions with finite energy to a general class of Dirichlet problems
• Existence and Regularity of Extremal Metrics for the Conformal Dirichlet-to-Robin Map

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