Local boundedness, maximum principles, and continuity of solutions to infinitely degenerate elliptic equations

2015/06/30 by Korobenko, Lyudmila, Rios, Cristian, Sawyer, Eric +1 · 3 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1506.09203

Abstract

We develop subrepresentation inequalities for infinitely degenerate metrics, and obtain corresponding Poincare and Sobolev inequalities. We then derive conditions on the degenerate metric under which weak solutions to associated infinitely degenerate equations with rough coefficients are locally bounded, satisfy a maximum principle, or are continuous. As an application we obtain W-hypoellipticity of certain infinitely degenerate quasilinear equations with smooth coefficients having mild nonlinearities and degeneracies.

Cited by

• The weak maximum principle for solutions of degenerate elliptic equations with lower order terms
• Existence and uniqueness of solutions of degenerate elliptic equations with lower order terms
• Continuity of weak solutions to rough infinitely degenerate equations

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