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Open Access Research

On the maximum principle for elliptic operators in weighted spaces

Loredana Caso* and Roberta D’Ambrosio

Author Affiliations

Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II, I - 84084, Fisciano, Italy

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Boundary Value Problems 2014, 2014:91  doi:10.1186/1687-2770-2014-91

Published: 6 May 2014


We establish a maximum principle for subsolutions of second order elliptic equations. In particular, we consider some linear operators with leading coefficients locally VMO, while the other coefficients and the boundary conditions involve a suitable weight function.

MSC: 35J25, 35R05, 35B50.

elliptic operators; VMO-coefficients; weighted Sobolev spaces; maximum principle