Regularity of solutions of divergence form elliptic equations
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- by Maria Alessandra Ragusa PDF
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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 $VMO.$References
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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
- Received by editor(s): April 6, 1998
- Published electronically: July 7, 1999
- Communicated by: Lesley M. Sibner
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 533-540
- MSC (1991): Primary 35B65, 32A37, 31B10; Secondary 46E35, 42B20
- DOI: https://doi.org/10.1090/S0002-9939-99-05165-5
- MathSciNet review: 1641085
Dedicated: Dedicated to the memory of two friends Filippo Chiarenza and Gene Fabes