Regularizing effects concerning elliptic equations with a superlinear gradient term
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2019
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910792966733824 |
|---|---|
| author | Balado, Marta Latorre Magliocca, Martina de León, Sergio Segura |
| author_facet | Balado, Marta Latorre Magliocca, Martina de León, Sergio Segura |
| contents | 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 $L^m(Ω)$ with $1\le m <\frac{N}{2}$ as well as measure data instead of $L^1$-data, so that unbounded solutions are expected. Our aim is, given $1\le m<\frac N2$ 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 $q=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_02643 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Regularizing effects concerning elliptic equations with a superlinear gradient term Balado, Marta Latorre Magliocca, Martina de León, Sergio Segura Analysis of PDEs 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 $L^m(Ω)$ with $1\le m <\frac{N}{2}$ as well as measure data instead of $L^1$-data, so that unbounded solutions are expected. Our aim is, given $1\le m<\frac N2$ 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 $q=2$. |
| title | Regularizing effects concerning elliptic equations with a superlinear gradient term |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1910.02643 |