Arkiv för Matematik

  • Ark. Mat.
  • Volume 48, Number 2 (2010), 253-287.

Solvability of elliptic systems with square integrable boundary data

Pascal Auscher, Andreas Axelsson, and Alan McIntosh

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Abstract

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 L2 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.

Article information

Source
Ark. Mat., Volume 48, Number 2 (2010), 253-287.

Dates
Received: 1 October 2008
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907113

Digital Object Identifier
doi:10.1007/s11512-009-0108-2

Mathematical Reviews number (MathSciNet)
MR2672609

Zentralblatt MATH identifier
1205.35082

Rights
2009 © Institut Mittag-Leffler

Citation

Auscher, Pascal; Axelsson, Andreas; McIntosh, Alan. Solvability of elliptic systems with square integrable boundary data. Ark. Mat. 48 (2010), no. 2, 253--287. doi:10.1007/s11512-009-0108-2. https://projecteuclid.org/euclid.afm/1485907113


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