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arXiv · 1212.3931

On $L^2$ Solvability of BVPs for elliptic systems

Pascal Auscher·Alan McIntosh·Mihalis Mourgoglou
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Abstract

In this article we prove solvability results for $L^2$ boundary value problems of some elliptic systems $Lu=0$ on the upper half-space $\R^{n+1}_{+}, n\ge 1$, with transversally independent coefficients. We use the first order formalism introduced by Auscher-Axelsson-McIntosh and further developed with a better understanding of the classes of solutions in the subsequent work of Auscher-Axelsson. The interesting fact is that we prove only half of the Rellich boundary inequality without knowing the other half.

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Pascal Auscher, Alan McIntosh, Mihalis Mourgoglou. 2012-12-17. On $L^2$ Solvability of BVPs for elliptic systems. https://arxiv.org/abs/1212.3931

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