Elliptic problems with superlinear convection terms
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916089253855232 |
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| author | Boccardo, L. Buccheri, S. Cirmi, G. R. |
| author_facet | Boccardo, L. Buccheri, S. Cirmi, G. R. |
| contents | In this manuscript we deal with elliptic equations with superlinear first order terms in divergence form of the following type \[ -\mbox{div}(M(x)\nabla u)= -\mbox{div}(h(u)E(x))+f(x), \] where $M$ is a bounded elliptic matrix, the vector field $E$ and the function $f$ belong to suitable Lebesgue spaces, and the function $s\to h(s)$ features a superlinear growth at infinity. We provide some existence and non existence results for solutions to the associated Dirichlet problem and a comparison principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06642 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Elliptic problems with superlinear convection terms Boccardo, L. Buccheri, S. Cirmi, G. R. Analysis of PDEs In this manuscript we deal with elliptic equations with superlinear first order terms in divergence form of the following type \[ -\mbox{div}(M(x)\nabla u)= -\mbox{div}(h(u)E(x))+f(x), \] where $M$ is a bounded elliptic matrix, the vector field $E$ and the function $f$ belong to suitable Lebesgue spaces, and the function $s\to h(s)$ features a superlinear growth at infinity. We provide some existence and non existence results for solutions to the associated Dirichlet problem and a comparison principle. |
| title | Elliptic problems with superlinear convection terms |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.06642 |