Solvability of elliptic systems with square integrable boundary data

Pascal Auscher; Andreas Axelsson; Alan McIntosh

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arXiv · 0809.4968

Solvability of elliptic systems with square integrable boundary data

Pascal Auscher·Andreas Axelsson·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 $L_2$ 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 PDEs and as an example we prove perturbation results for boundary value problems for differential forms.

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Pascal Auscher, Andreas Axelsson, Alan McIntosh. 2008-09-29. Solvability of elliptic systems with square integrable boundary data. https://arxiv.org/abs/0809.4968

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