Representation and uniqueness for boundary value elliptic problems via first order systems
Pascal Auscher
Université de Picardie-Jules Verne, Amiens, France and Université Paris-Sud, FranceMihalis Mourgoglou
Universidad del País Vasco, Leioa, Spain and Ikerbasque, Basque Foundation for Science, Bilbao, Spain
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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 this article
Pascal Auscher, Mihalis Mourgoglou, Representation and uniqueness for boundary value elliptic problems via first order systems. Rev. Mat. Iberoam. 35 (2019), no. 1, pp. 241–315
DOI 10.4171/RMI/1054