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Existence and regularity results for nonlinear elliptic equations in Orlicz spaces

Giuseppina Barletta
Dec 2022
摘要
We are concerned with the existence and regularity of the solutions to theDirichlet problem, for a class of quasilinear elliptic equations driven by ageneral differential operator, depending on $(x,u,\nabla u)$, and with aconvective term $f$. The assumptions on the members of the equation areformulated in terms of Young's functions, therefore we work in theOrlicz-Sobolev spaces. After establishing some auxiliary properties, that seemnew in our context, we present two existence and two regularity results. Weconclude with several examples.
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