Existence and regularity results for nonlinear elliptic equations in Orlicz spaces

Giuseppina Barletta

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arXiv · 2212.04779

Existence and regularity results for nonlinear elliptic equations in Orlicz spaces

Giuseppina Barletta

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Abstract

We are concerned with the existence and regularity of the solutions to the Dirichlet problem, for a class of quasilinear elliptic equations driven by a general differential operator, depending on $(x,u,\nabla u)$, and with a convective term $f$. The assumptions on the members of the equation are formulated in terms of Young's functions, therefore we work in the Orlicz-Sobolev spaces. After establishing some auxiliary properties, that seem new in our context, we present two existence and two regularity results. We conclude with several examples.

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Giuseppina Barletta. 2022-12-09. Existence and regularity results for nonlinear elliptic equations in Orlicz spaces. https://arxiv.org/abs/2212.04779

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