Regularizing effect in some Mingione’s double phase problems with very singular data
><p>In this paper we study the existence of solutions of the Dirichlet problem associated to the following nonlinear PDE</p> <p class="disp_formula">$ \begin{equation*} { } -{{{\rm{\;div}}}}\big(a(x)\,\nabla u|\nabla u|^{p-2}\big) -{{{\rm{\;div}}}}\big( |u|^{(r-1)\l...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023069?viewType=HTML |
| _version_ | 1797659064073715712 |
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| author | Lucio Boccardo Giuseppa Rita Cirmi |
| author_facet | Lucio Boccardo Giuseppa Rita Cirmi |
| author_sort | Lucio Boccardo |
| collection | DOAJ |
| description | ><p>In this paper we study the existence of solutions of the Dirichlet problem associated to the following nonlinear PDE</p>
<p class="disp_formula">$ \begin{equation*} { } -{{{\rm{\;div}}}}\big(a(x)\,\nabla u|\nabla u|^{p-2}\big) -{{{\rm{\;div}}}}\big( |u|^{(r-1)\lambda+1}\nabla u|\nabla u|^{\lambda-2}\big) = f \end{equation*} $</p>
<p>where $ 1 < \lambda \leq p $, $ r > 1 $ and $ f \in L^1(\Omega) $.</p> |
| first_indexed | 2024-03-11T18:08:33Z |
| format | Article |
| id | doaj.art-b4830e6eeec54bf6b5fecaca75ba7f56 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-11T18:08:33Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-b4830e6eeec54bf6b5fecaca75ba7f562023-10-17T01:21:47ZengAIMS PressMathematics in Engineering2640-35012023-09-015311510.3934/mine.2023069Regularizing effect in some Mingione’s double phase problems with very singular dataLucio Boccardo0Giuseppa Rita Cirmi11. Istituto Lombardo & Sapienza Università di Roma, Piazzale A. Moro 5, 00185 Roma, Italy2. Università di Catania, Dipartimento di Matematica e Informatica, Viale A. Doria 6, 95125 Catania, Italy><p>In this paper we study the existence of solutions of the Dirichlet problem associated to the following nonlinear PDE</p> <p class="disp_formula">$ \begin{equation*} { } -{{{\rm{\;div}}}}\big(a(x)\,\nabla u|\nabla u|^{p-2}\big) -{{{\rm{\;div}}}}\big( |u|^{(r-1)\lambda+1}\nabla u|\nabla u|^{\lambda-2}\big) = f \end{equation*} $</p> <p>where $ 1 < \lambda \leq p $, $ r > 1 $ and $ f \in L^1(\Omega) $.</p> https://www.aimspress.com/article/doi/10.3934/mine.2023069?viewType=HTMLnonlinear elliptic equationsweak solutionsdouble phase problemssingular dataregularity |
| spellingShingle | Lucio Boccardo Giuseppa Rita Cirmi Regularizing effect in some Mingione’s double phase problems with very singular data Mathematics in Engineering nonlinear elliptic equations weak solutions double phase problems singular data regularity |
| title | Regularizing effect in some Mingione’s double phase problems with very singular data |
| title_full | Regularizing effect in some Mingione’s double phase problems with very singular data |
| title_fullStr | Regularizing effect in some Mingione’s double phase problems with very singular data |
| title_full_unstemmed | Regularizing effect in some Mingione’s double phase problems with very singular data |
| title_short | Regularizing effect in some Mingione’s double phase problems with very singular data |
| title_sort | regularizing effect in some mingione s double phase problems with very singular data |
| topic | nonlinear elliptic equations weak solutions double phase problems singular data regularity |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2023069?viewType=HTML |
| work_keys_str_mv | AT lucioboccardo regularizingeffectinsomemingionesdoublephaseproblemswithverysingulardata AT giusepparitacirmi regularizingeffectinsomemingionesdoublephaseproblemswithverysingulardata |