Solvability of elliptic systems with square integrable boundary data

We consider second order elliptic divergence form systems with complex measurable coefficients A that are independent of the transversal coordinate, and prove that the set of A for which the boundary value problem with L 2 Dirichlet or Neumann data is well posed, is an open set. Furthermore we prove...

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Bibliographic Details
Published inArkiv för matematik Vol. 48; no. 2; pp. 253 - 287
Main Authors Auscher, Pascal, Axelsson, Andreas, McIntosh, Alan
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 2010
Subjects
MATEMATIK
MATHEMATICS
Mathematics and Statistics
Neumann Problem
Dirichlet Problem
Elliptic System
Boundary Data
Lipschitz Domain
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Summary:We consider second order elliptic divergence form systems with complex measurable coefficients A that are independent of the transversal coordinate, and prove that the set of A for which the boundary value problem with L 2 Dirichlet or Neumann data is well posed, is an open set. Furthermore we prove that these boundary value problems are well posed when A is either Hermitean, block or constant. Our methods apply to more general systems of partial differential equations and as an example we prove perturbation results for boundary value problems for differential forms.
ISSN:0004-2080
1871-2487
1871-2487
DOI:10.1007/s11512-009-0108-2