Continuity estimates for -Laplace type operators in Orlicz–Zygmund spaces

  • Fernando Farroni

    Università Telematica Pegaso, Napoli, Italy

Abstract

We study the Dirichlet problem

in a bounded Lipschitz domain , with . The vector field satisfies the typical growth and coercivity conditions of the -Laplacian type operator with . We prove existence and uniqueness results in the case the vector field belongs to the Orlicz–Zygmund space and or and . In particular, the gradient of the solution belongs to . Further, we provide estimates implying the continuity of the operator which carries any given into the gradient field of the solution.

Cite this article

Fernando Farroni, Continuity estimates for -Laplace type operators in Orlicz–Zygmund spaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 27 (2016), no. 3, pp. 335–354

DOI 10.4171/RLM/738