Regularity of solutions of divergence form elliptic equations

The aim of this paper is to study local regularity in the Morrey spaces L^{p,\lambda} of the first derivatives of the solutions of an elliptic second order equation in divergence form \begin{equation*} {\mathcal L} u \equiv -\sum_{i,j=1}^n (a_{ij}(x) u_{x_i})_{x_j} =div f(x)\quad \text{for a.a.} x\i...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2000-02, Vol.128 (2), p.533-540
Main Author: Ragusa, Maria Alessandra
Format: Article
Language:English
Subjects:
Coefficients
Elliptic equations
Function discontinuity
Mathematical functions
Mathematical integrals
Mathematical theorems
Mathematics
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Summary:The aim of this paper is to study local regularity in the Morrey spaces L^{p,\lambda} of the first derivatives of the solutions of an elliptic second order equation in divergence form \begin{equation*} {\mathcal L} u \equiv -\sum_{i,j=1}^n (a_{ij}(x) u_{x_i})_{x_j} =div f(x)\quad \text{for a.a.} x\in \Omega, \end{equation*} where f is assumed to be in some L^{p,\lambda} spaces and the coefficients a_{ij} belong to the space VMO.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-99-05165-5