-solvability of the Dirichlet problem for a class of elliptic equations with discontinuous coefficients
Flavia Giannetti
Università degli Studi di Napoli Federico II, ItalyGioconda Moscariello
Università degli Studi di Napoli Federico II, Italy
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Abstract
We study the Dirichlet problem for the second order elliptic equation
in a bounded regular domain . We assume that and that the coefficients are measurable and bounded functions with the first derivatives in the Marcinkiewicz class weak and having a sufficiently small distance to . Under these assumptions we prove the solvability of the problem in , where . An higher integrability result for the gradient of the solution is achieved when .
Cite this article
Flavia Giannetti, Gioconda Moscariello, -solvability of the Dirichlet problem for a class of elliptic equations with discontinuous coefficients. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), no. 3, pp. 557–577
DOI 10.4171/RLM/820