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Regularity of solutions of divergence form elliptic equations

Author(s): Maria Alessandra Ragusa
Journal: Proc. Amer. Math. Soc. 128 (2000), 533-540.
MSC (1991): Primary 35B65, 32A37, 31B10; Secondary 46E35, 42B20
Posted: July 7, 1999
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Abstract: 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 $VMO.$

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Additional Information:

Maria Alessandra Ragusa
Affiliation: Dipartimento di Matematica, Università di Catania, Viale A. Doria, 6, 95125 Catania, Italy
Email: maragusa@dipmat.unict.it

DOI: 10.1090/S0002-9939-99-05165-5
PII: S 0002-9939(99)05165-5
Keywords: Elliptic equations, Morrey spaces, VMO
Received by editor(s): April 6, 1998
Posted: July 7, 1999
Dedicated: Dedicated to the memory of two friends Filippo Chiarenza and Gene Fabes
Communicated by: Lesley M. Sibner
Copyright of article: Copyright 1999, American Mathematical Society

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