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...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-04-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023081?viewType=HTML |
| _version_ | 1827631132140634112 |
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| author | Peter Bella Mathias Schäffner |
| author_facet | Peter Bella Mathias Schäffner |
| author_sort | Peter Bella |
| collection | DOAJ |
| description | 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 $. |
| first_indexed | 2024-03-09T14:16:44Z |
| format | Article |
| id | doaj.art-7314d8025e6a4904a1afefdec93b2de3 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-09T14:16:44Z |
| publishDate | 2023-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-7314d8025e6a4904a1afefdec93b2de32023-11-29T01:08:13ZengAIMS PressMathematics in Engineering2640-35012023-04-015512010.3934/mine.2023081Local boundedness for p-Laplacian with degenerate coefficientsPeter Bella 0Mathias Schäffner 11. Technische Universität Dortmund, Fakultät für Mathematik, Vogelpothsweg 87, 44227 Dortmund, Germany2. MLU Halle-Wittenberg, Institut für Mathematik, Theodor-Lieser-Straße 5, 06120 Halle (Saale), GermanyWe 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 $.https://www.aimspress.com/article/doi/10.3934/mine.2023081?viewType=HTMLelliptic regularitynonuniform ellipticitylocal boundednessunbounded solutionsweak solutions |
| spellingShingle | Peter Bella Mathias Schäffner Local boundedness for p-Laplacian with degenerate coefficients Mathematics in Engineering elliptic regularity nonuniform ellipticity local boundedness unbounded solutions weak solutions |
| title | Local boundedness for p-Laplacian with degenerate coefficients |
| title_full | Local boundedness for p-Laplacian with degenerate coefficients |
| title_fullStr | Local boundedness for p-Laplacian with degenerate coefficients |
| title_full_unstemmed | Local boundedness for p-Laplacian with degenerate coefficients |
| title_short | Local boundedness for p-Laplacian with degenerate coefficients |
| title_sort | local boundedness for p laplacian with degenerate coefficients |
| topic | elliptic regularity nonuniform ellipticity local boundedness unbounded solutions weak solutions |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2023081?viewType=HTML |
| work_keys_str_mv | AT peterbella localboundednessforplaplacianwithdegeneratecoefficients AT mathiasschaffner localboundednessforplaplacianwithdegeneratecoefficients |