Representation and uniqueness for boundary value elliptic problems via first order systems

被引：40

作者：

Auscher, Pascal ^{[1
,2
]}

Mourgoglou, Mihalis ^{[3
,4
,5
]}

机构：

[1] Univ Paris Saclay, CNRS, Univ Paris Sud, Lab Math Orsay, F-91405 Orsay, France

[2] Univ Picardie Jules Verne, UMR 7352, LAMFA, 33 Rue St Leu, F-80039 Amiens 1, France

[3] Univ Basque Country, Dept Matemat, Barrio Sarriena S-N, Leioa 48940, Spain

[4] Basque Fdn Sci, Ikerbasque, Bilbao, Spain

[5] Inst Hautes Etud Sci, 35 Route Chartres, F-91440 Bures Sur Yvette, France

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2019年 / 35卷 / 01期

关键词：

First order elliptic systems; Hardy spaces associated to operators; tent spaces; non-tangential maximal functions; second order elliptic systems; boundary layer operators; a priori estimates; Dirichlet and Neumann problems; extrapolation; SQUARE-ROOT PROBLEM; LAYER POTENTIALS; NEUMANN PROBLEM; FUNCTIONAL CALCULI; DIRICHLET PROBLEM; DIRAC OPERATORS; HARDY-SPACES; L-P; REGULARITY; SOLVABILITY;

D O I：

10.4171/RMI/1054

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given any elliptic system with t-independent coefficients in the upper-half space, we obtain representation and trace for the conormal gradient of solutions in the natural classes for the boundary value problems of Dirichlet and Neumann types with area integral control or non-tangential maximal control. The trace spaces are obtained in a natural range of boundary spaces which is parametrized by properties of some Hardy spaces. This implies a complete picture of uniqueness vs solvability and well-posedness.

引用

页码：241 / 315

页数：75

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