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arXiv · 2401.06642

Elliptic problems with superlinear convection terms

L. Boccardo·S. Buccheri·G. R. Cirmi
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Abstract

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.

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L. Boccardo, S. Buccheri, G. R. Cirmi. 2024-01-12. Elliptic problems with superlinear convection terms. https://arxiv.org/abs/2401.06642

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