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arXiv · 1307.8151

On Poisson operators and Dirichlet-Neumann maps in H^s for divergence form elliptic operators with Lipschitz coefficients

Yasunori Maekawa·Hideyuki Miura
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Abstract

We consider second order uniformly elliptic operators of divergence form in $\R^{d+1}$ whose coefficients are independent of one variable. Under the Lipschitz condition on the coefficients we characterize the domain of the Poisson operators and the Dirichlet-Neumann maps in the Sobolev space $H^s(\R^d)$ for each $s\in [0,1]$. Moreover, we also show a factorization formula for the elliptic operator in terms of the Poisson operator.

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Yasunori Maekawa, Hideyuki Miura. 2013-07-30. On Poisson operators and Dirichlet-Neumann maps in H^s for divergence form elliptic operators with Lipschitz coefficients. https://arxiv.org/abs/1307.8151

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