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arXiv · 1703.06962

The Neumann problem for higher order elliptic equations with symmetric coefficients

Ariel Barton·Steve Hofmann·Svitlana Mayboroda
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Abstract

In this paper we establish well posedness of the Neumann problem with boundary data in $L^2$ or the Sobolev space $\dot W^2_{-1}$, in the half space, for linear elliptic differential operators with coefficients that are constant in the vertical direction and in addition are self adjoint. This generalizes the well known well-posedness result of the second order case and is based on a higher order and one sided version of the classic Rellich identity, and is the first known well posedness result for a higher order operator with rough variable coefficients and boundary data in a Lebesgue or Sobolev space.

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Ariel Barton, Steve Hofmann, Svitlana Mayboroda. 2017-03-20. The Neumann problem for higher order elliptic equations with symmetric coefficients. https://arxiv.org/abs/1703.06962

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