Existence and regularity results for nonlinear elliptic equations in Orlicz spaces

2022/12/09 by Barletta, Giuseppina
#35J25 #35J60 #46E30 #47J05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.04779

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,∇ 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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