On domain of Poisson operators and factorization for divergence form elliptic operators

Yasunori Maekawa; Hideyuki Miura

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arXiv · 1307.6517

On domain of Poisson operators and factorization for divergence form elliptic operators

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. For such a class of operators we establish a factorization into a product of first order operators related with Poisson operators and Dirichlet-Neumann maps. Consequently, we obtain a solution formula for the inhomogeneous elliptic boundary value problem in the half space, which is useful to show the existence of solutions in a wider class of inhomogeneous data. We also establish $L^2$ solvability of boundary value problems for a new class of the elliptic operators.

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Yasunori Maekawa, Hideyuki Miura. 2013-07-24. On domain of Poisson operators and factorization for divergence form elliptic operators. https://arxiv.org/abs/1307.6517

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