Regularity and symmetry results for the vectorial p-Laplacian
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916156370059264 |
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| author | Montoro, Luigi Muglia, Luigi Sciunzi, Berardino Vuono, Domenico |
| author_facet | Montoro, Luigi Muglia, Luigi Sciunzi, Berardino Vuono, Domenico |
| contents | We obtain some regularity results for solutions to vectorial $p$-Laplace equations $$ -{\boldsymbol Δ}_p{\boldsymbol u}=-\operatorname{\bf div}(|D{\boldsymbol u}|^{p-2}D{\boldsymbol u}) = {\boldsymbol f}(x,{\boldsymbol u})\,\, \mbox{ in $Ω$}\,.$$ More precisely we address the issue of second order estimates for the stress field. As a consequence of our regularity results we deduce a weighted Sobolev inequality that leads to weak comparison principles. As a corollary we run over the moving plane technique to deduce symmetry and monotonicity results for the solutions, under suitable assumptions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_05388 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Regularity and symmetry results for the vectorial p-Laplacian Montoro, Luigi Muglia, Luigi Sciunzi, Berardino Vuono, Domenico Analysis of PDEs 35J92, 35B65, 35B51, 35B06 We obtain some regularity results for solutions to vectorial $p$-Laplace equations $$ -{\boldsymbol Δ}_p{\boldsymbol u}=-\operatorname{\bf div}(|D{\boldsymbol u}|^{p-2}D{\boldsymbol u}) = {\boldsymbol f}(x,{\boldsymbol u})\,\, \mbox{ in $Ω$}\,.$$ More precisely we address the issue of second order estimates for the stress field. As a consequence of our regularity results we deduce a weighted Sobolev inequality that leads to weak comparison principles. As a corollary we run over the moving plane technique to deduce symmetry and monotonicity results for the solutions, under suitable assumptions. |
| title | Regularity and symmetry results for the vectorial p-Laplacian |
| topic | Analysis of PDEs 35J92, 35B65, 35B51, 35B06 |
| url | https://arxiv.org/abs/2311.05388 |