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On the Uniqueness ofL 2-solutions in half-space of certain differential equations

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Abstract

Square integrable solutions to the equation{−∂ 2/∂y2 + P(Dx)+b(y)−λ}u(x, y) = f(x, y) are considered in the half-spacey>0, x ∈ℝn, whereP(D x) is a constant coefficient operator. Under suitable conditions on limy→0u(x, y), b(y), f(x, y) and λ, it is shown that suppu = suppf. This generalizes a result due to Walter Littman.

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Authors and Affiliations

  1. Department of Mathematics, Technion—Israel Institute of Technology, Haifa, Israel

    Matania Ben-Artzi

  2. Department of Mathematics, Northwestern University, 60201, Evanston, IL, USA

    Allen Devinatz

Authors
  1. Matania Ben-Artzi
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  2. Allen Devinatz
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Additional information

Communicated by D. Kinderlehrer

Research partially supported by USNSF Grant 79-02538-A02.

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Ben-Artzi, M., Devinatz, A. On the Uniqueness ofL 2-solutions in half-space of certain differential equations. Appl Math Optim 9, 97–109 (1982). https://doi.org/10.1007/BF01460120

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