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Keywords:
quasi-linear problems; $p$-Laplacian; $L_\infty$-estimates; non-smooth domains; Moser iterations
Summary:
This lecture follows a joint result of the speaker and Daniel Daners. To make the exposition clear and transparent we concentrate here only on the $L_\infty$-estimates for weak solutions for the $p$-Laplacian with all standard boundary conditions on possibly non-smooth domains. We present $C^{1,\alpha}$-regularity and maximum principle for weak solutions as an application. We also prove existence, continuity and compactness of the resolvent operator.

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