Representation and uniqueness for boundary value elliptic problems via first order systems
Classical Analysis and ODEs
2015-11-06 v2 Analysis of PDEs
Functional Analysis
Abstract
Given any elliptic system with -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.
Cite
@article{arxiv.1404.2687,
title = {Representation and uniqueness for boundary value elliptic problems via first order systems},
author = {Pascal Auscher and Mihalis Mourgoglou},
journal= {arXiv preprint arXiv:1404.2687},
year = {2015}
}
Comments
submitted, 70 pages. A number of maths typos have been eliminated