Regularizing effects concerning elliptic equations with a superlinear gradient term
We consider the homogeneous Dirichlet problem for an elliptic equation driven by a linear operator with discontinuous coefficients and having a subquadratic gradient term. This gradient term behaves as g(u)|\nabla u|^q, where 1<q<2 and g(s) is a continuous function. Data belong to L^m with 1\l...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universidad Rey Juan Carlos |
| Repositorio: | BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos |
| OAI Identifier: | oai:burjcdigital.urjc.es:10115/31913 |
| Acesso em linha: | https://hdl.handle.net/10115/31913 |
| Access Level: | acceso embargado |
| Palavra-chave: | Quasilinear elliptic equations Gradient term with superlinear growth Renormalized solutions Measure data |
| Resumo: | We consider the homogeneous Dirichlet problem for an elliptic equation driven by a linear operator with discontinuous coefficients and having a subquadratic gradient term. This gradient term behaves as g(u)|\nabla u|^q, where 1<q<2 and g(s) is a continuous function. Data belong to L^m with 1\le m <N/2 as well as measure data instead of $L^1$-data, so that unbounded solutions are expected. Our aim is, given 1\le m<N/2 and 1<q<2, to find the suitable behaviour of $g$ close to infinity which leads to existence for our problem. We show that the presence of g has a regularizing effect in the existence and summability of the solution. Moreover, our results adjust with continuity with known results when either g(s) is constant or q=2. |
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