On L2 Solvability of BVPs for Elliptic Systems

Pascal Auscher; Alan McIntosh; Mihalis Mourgoglou

doi:10.1007/s00041-013-9266-5

On L² Solvability of BVPs for Elliptic Systems

Pascal Auscher^*, Alan McIntosh, Mihalis Mourgoglou

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

In this article we prove solvability results for L² boundary value problems of some elliptic systems Lu=0 on the upper half-space ℝⁿ⁺¹₊ n≥1, with transversally independent coefficients. We use the first order formalism introduced by Auscher-Axelsson-McIntosh and further developed with a better understanding of the classes of solutions in the subsequent work of Auscher-Axelsson. The interesting fact is that we prove only half of the Rellich boundary inequality without knowing the other half.

Original language	English
Pages (from-to)	478-494
Number of pages	17
Journal	Journal of Fourier Analysis and Applications
Volume	19
Issue number	3
DOIs	https://doi.org/10.1007/s00041-013-9266-5
Publication status	Published - Jun 2013

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title = "On L2 Solvability of BVPs for Elliptic Systems",

abstract = "In this article we prove solvability results for L2 boundary value problems of some elliptic systems Lu=0 on the upper half-space ℝn+1+ n≥1, with transversally independent coefficients. We use the first order formalism introduced by Auscher-Axelsson-McIntosh and further developed with a better understanding of the classes of solutions in the subsequent work of Auscher-Axelsson. The interesting fact is that we prove only half of the Rellich boundary inequality without knowing the other half.",

keywords = "Dirichlet and Neumann problems, Elliptic systems, Non-tangential maximal functions, Square functions, Tb theorems, Variational solutions",

author = "Pascal Auscher and Alan McIntosh and Mihalis Mourgoglou",

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doi = "10.1007/s00041-013-9266-5",

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T1 - On L2 Solvability of BVPs for Elliptic Systems

AU - Auscher, Pascal

AU - McIntosh, Alan

AU - Mourgoglou, Mihalis

PY - 2013/6

Y1 - 2013/6

N2 - In this article we prove solvability results for L2 boundary value problems of some elliptic systems Lu=0 on the upper half-space ℝn+1+ n≥1, with transversally independent coefficients. We use the first order formalism introduced by Auscher-Axelsson-McIntosh and further developed with a better understanding of the classes of solutions in the subsequent work of Auscher-Axelsson. The interesting fact is that we prove only half of the Rellich boundary inequality without knowing the other half.

AB - In this article we prove solvability results for L2 boundary value problems of some elliptic systems Lu=0 on the upper half-space ℝn+1+ n≥1, with transversally independent coefficients. We use the first order formalism introduced by Auscher-Axelsson-McIntosh and further developed with a better understanding of the classes of solutions in the subsequent work of Auscher-Axelsson. The interesting fact is that we prove only half of the Rellich boundary inequality without knowing the other half.

KW - Dirichlet and Neumann problems

KW - Elliptic systems

KW - Non-tangential maximal functions

KW - Square functions

KW - Tb theorems

KW - Variational solutions

UR - http://www.scopus.com/inward/record.url?scp=84877049084&partnerID=8YFLogxK

U2 - 10.1007/s00041-013-9266-5

DO - 10.1007/s00041-013-9266-5

M3 - Article

SN - 1069-5869

VL - 19

SP - 478

EP - 494

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 3

ER -

On L² Solvability of BVPs for Elliptic Systems

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