Elliptic problems with superlinear convection terms

2024/01/12 by Lucio Boccardo, Boccardo, L., Stefano Buccheri +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2401.06642

openalex publication_date 2024/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this manuscript we deal with elliptic equations with superlinear first order terms in divergence form of the following type -div(M(x)∇ u)= -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→ 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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• Parabolic problems with slightly superlinear convection terms

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