The L p -Solvability of the Dirichlet Problem for Planar Elliptic Equations, Sharp Results |
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| Authors: | Carlo Sbordone Gabriella Zecca |
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| Affiliation: | 1. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Via Cintia—Complesso Universitario Monte S. Angelo, 80126, Napoli, Italy
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| Abstract: | Assume that the elliptic operator L=div (A(x)∇) is L p -resolutive, p>1, on the unit disc mathbbD ì mathbb R2mathbb{D}subset mathbb {R}^{2} . This means that the Dirichlet problem | $left{{l@{quad}l}Lu=0&mbox{in }mathbb{D},[3pt]u=g&mbox{on }partialmathbb{D}right.$left{begin{array}{l@{quad}l}Lu=0&mbox{in }mathbb{D},[3pt]u=g&mbox{on }partialmathbb{D}end{array}right. |
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