Local boundedness for p-Laplacian with degenerate coefficients
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-04-01
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| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023081?viewType=HTML |
| Summary: | 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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| ISSN: | 2640-3501 |