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The L-p Dirichlet problem for second-order, non-divergence form operators: solvability and perturbation results

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http://www.sciencedirect.com/science/article/pii/S0022123611001996
Original languageEnglish
Pages (from-to)1753-1774
Number of pages22
JournalJournal of functional analysis
Volume261
Issue number7
DOIs
Publication statusPublished - 1 Oct 2011

Abstract

We establish Dahlberg's perturbation theorem for non-divergence form operators L = A del(2). If L-0 and L-1 are two operators on a Lipschitz domain such that the L-p Dirichlet problem for the operator L-0 is solvable for some p is an element of (1, infinity) and the coefficients of the two operators are sufficiently close in the sense of Carleson measure, then the L-p Dirichlet problem for the operator L-1 is solvable for the same p. This is a refinement of the A(infinity) version of this result proved by Rios (2003) in [10]. As a consequence we also improve a result from Dindos et al. (2007) [4] for the L-p solvability of non-divergence form operators (Theorem 3.2) by substantially weakening the condition required on the coefficients of the operator. The improved condition is exactly the same one as is required for divergence form operators L = div A del. (C) 2011 Elsevier Inc. All rights reserved.

    Research areas

  • Second order non-divergence form elliptic operators, Perturbation theorem, L-p solvability, Dirichlet problem, ELLIPTIC-EQUATIONS, COEFFICIENTS, DRIFT

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