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

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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. 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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Author notes

  1. Yasunori Maekawa

    Present address: Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan

Authors and Affiliations

  1. Mathematical Institute, Tohoku University, 6-3 Aoba, Aramaki, Aoba, Sendai, 980-8578, Japan

    Yasunori Maekawa

  2. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro, Tokyo, 152-8552, Japan

    Hideyuki Miura

Authors
  1. Yasunori Maekawa
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  2. Hideyuki Miura
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Correspondence to Hideyuki Miura.

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Maekawa, Y., Miura, H. On domain of Poisson operators and factorization for divergence form elliptic operators. manuscripta math. 152, 459–512 (2017). https://doi.org/10.1007/s00229-016-0858-7

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  • DOI: https://doi.org/10.1007/s00229-016-0858-7

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