Continuity estimates for -Laplace type operators in Orlicz–Zygmund spaces
Fernando Farroni
Università Telematica Pegaso, Napoli, Italy
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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