# ANNALES DE L'INSTITUT FOURIER

Dirichlet and Neumann boundary values of solutions to higher order elliptic equations
Annales de l'Institut Fourier, to appear, 52 p.

We show that if $u$ is a solution to a linear elliptic differential equation of order $2m\ge 2$ in the half-space with $t$-independent coefficients, and if $u$ satisfies certain area integral estimates, then the Dirichlet and Neumann boundary values of $u$ exist and lie in a Lebesgue space ${L}^{p}\left({ℝ}^{n}\right)$ or Sobolev space ${\stackrel{˙}{W}}_{±1}^{p}\left({ℝ}^{n}\right)$. Even in the case where $u$ is a solution to a second order equation, our results are new for certain values of $p$.

On montre que si $u$ est une solution d’une équation aux dérivées partielles elliptique d’ordre $2m\ge 2$ dans le demi-espace à coefficients indépendants de $t$, et $u$ satisfait certaines conditions d’intégrales de surface, alors les données aux frontières de Dirichlet et de Neumann de $u$ existent et appartiennent à un espace de Lebesgue ${L}^{p}\left({ℝ}^{n}\right)$ ou un espace de Sobolev ${\stackrel{˙}{W}}_{±1}^{p}\left({ℝ}^{n}\right)$. Même dans le cas où $u$ est une solution d’une équation de second ordre, nos résultats sont nouveaux pour certaines valeurs de $p$.

Accepted : 2018-06-12
Classification:  35J67,  35J30,  31B10
Keywords: Elliptic equation, higher order differential equation, Dirichlet boundary values, Neumann boundary values
@unpublished{AIF_0__0_0_A4_0,
author = {Barton, Ariel and Hofmann, Steve and Mayboroda, Svitlana},
title = {Dirichlet and Neumann boundary values of solutions to higher order elliptic equations},
note = {to appear in \emph{Annales de l'Institut Fourier}},
}

Dirichlet and Neumann boundary values of solutions to higher order elliptic equations. Annales de l'Institut Fourier, to appear, 52 p.

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