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arXiv · 1506.09203

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

Lyudmila Korobenko·Cristian Rios·Eric Sawyer·Ruipeng Shen
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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.

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Lyudmila Korobenko, Cristian Rios, Eric Sawyer, Ruipeng Shen. 2015-06-30. Local boundedness, maximum principles, and continuity of solutions to infinitely degenerate elliptic equations. https://arxiv.org/abs/1506.09203

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