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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| Institution: | 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 R2\mathbb{D}\subset \mathbb {R}^{2}
. This means that the Dirichlet problem
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$\left\{{l@{\quad}l}Lu=0&\mbox{in }\mathbb{D},\\3pt]u=g&\mbox{on }\partial\mathbb{D}\right.$\left\{\begin{array}{l@{\quad}l}Lu=0&\mbox{in }\mathbb{D},\\3pt]u=g&\mbox{on }\partial\mathbb{D}\end{array}\right. |
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| Keywords: | |
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