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arXiv · 2209.05976

Local boundedness for $p$-Laplacian with degenerate coefficients

Peter Bella·Mathias Schäffner
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Abstract

We study local boundedness for subsolutions of nonlinear nonuniformly elliptic equations whose prototype is given by $\nabla \cdot (\lambda |\nabla u|^{p-2}\nabla u)=0$, where the variable coefficient $0\leq\lambda$ and its inverse $\lambda^{-1}$ are allowed to be unbounded. Assuming certain integrability conditions on $\lambda$ and $\lambda^{-1}$ depending on $p$ and the dimension, we show local boundedness. Moreover, we provide counterexamples to regularity showing that the integrability conditions are optimal for every $p>1$.

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Peter Bella, Mathias Schäffner. 2022-09-13. Local boundedness for $p$-Laplacian with degenerate coefficients. https://arxiv.org/abs/2209.05976

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