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

Maekawa, Yasunori; Miura, Hideyuki

doi:10.1090/tran/6571

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

We consider second order uniformly elliptic operators of divergence form in $\mathbb {R}^{d+1}$ 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 $H^s(\mathbb {R}^d)$ 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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