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Solvability of elliptic systems with square integrable boundary data

Pascal Auscher Université Paris-Sud 11 UMR 8628 du CNRS, Orsay Cedex, France Andreas Axelsson Department of Mathematics, Stockholm University Alan McIntosh Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University

TBD mathscidoc:1701.333170

Arkiv for Matematik, 48, (2), 253-287, 2008.10
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.
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@inproceedings{pascal2008solvability,
  title={Solvability of elliptic systems with square integrable boundary data},
  author={Pascal Auscher, Andreas Axelsson, and Alan McIntosh},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203627376588979},
  booktitle={Arkiv for Matematik},
  volume={48},
  number={2},
  pages={253-287},
  year={2008},
}
Pascal Auscher, Andreas Axelsson, and Alan McIntosh. Solvability of elliptic systems with square integrable boundary data. 2008. Vol. 48. In Arkiv for Matematik. pp.253-287. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203627376588979.
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