We show that if is a solution to a linear elliptic differential equation of order in the half-space with -independent coefficients, and if satisfies certain area integral estimates, then the Dirichlet and Neumann boundary values of exist and lie in a Lebesgue space or Sobolev space . Even in the case where is a solution to a second order equation, our results are new for certain values of .
On montre que si est une solution d’une équation aux dérivées partielles elliptique d’ordre dans le demi-espace à coefficients indépendants de , et satisfait certaines conditions d’intégrales de surface, alors les données aux frontières de Dirichlet et de Neumann de existent et appartiennent à un espace de Lebesgue ou un espace de Sobolev . Même dans le cas où est une solution d’une équation de second ordre, nos résultats sont nouveaux pour certaines valeurs de .
Accepted:
Published online:
DOI: 10.5802/aif.3278
Keywords: Elliptic equation, higher order differential equation, Dirichlet boundary values, Neumann boundary values
Mot clés : Equation elliptique, équation différentielle d’ordre supérieur, données aux frontières de type Dirichlet, données aux frontières de type Neumann
Barton, Ariel 1; Hofmann, Steve 2; Mayboroda, Svitlana 3
@article{AIF_2019__69_4_1627_0, author = {Barton, Ariel and Hofmann, Steve and Mayboroda, Svitlana}, title = {Dirichlet and {Neumann} boundary values of solutions to higher order elliptic equations}, journal = {Annales de l'Institut Fourier}, pages = {1627--1678}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {69}, number = {4}, year = {2019}, doi = {10.5802/aif.3278}, zbl = {1394.35159}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3278/} }
TY - JOUR AU - Barton, Ariel AU - Hofmann, Steve AU - Mayboroda, Svitlana TI - Dirichlet and Neumann boundary values of solutions to higher order elliptic equations JO - Annales de l'Institut Fourier PY - 2019 SP - 1627 EP - 1678 VL - 69 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3278/ DO - 10.5802/aif.3278 LA - en ID - AIF_2019__69_4_1627_0 ER -
%0 Journal Article %A Barton, Ariel %A Hofmann, Steve %A Mayboroda, Svitlana %T Dirichlet and Neumann boundary values of solutions to higher order elliptic equations %J Annales de l'Institut Fourier %D 2019 %P 1627-1678 %V 69 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3278/ %R 10.5802/aif.3278 %G en %F AIF_2019__69_4_1627_0
Barton, Ariel; Hofmann, Steve; Mayboroda, Svitlana. Dirichlet and Neumann boundary values of solutions to higher order elliptic equations. Annales de l'Institut Fourier, Volume 69 (2019) no. 4, pp. 1627-1678. doi : 10.5802/aif.3278. https://aif.centre-mersenne.org/articles/10.5802/aif.3278/
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