Representation and uniqueness for boundary value elliptic problems via first order systems
- Pascal Auscher 1
- Mihalis Mourgoglou 2
- 1 Université de Picardie-Jules Verne, Amiens
- 2 Universidad del País Vasco, Leioa
ISSN: 0213-2230
Any de publicació: 2019
Volum: 35
Número: 1
Pàgines: 241-315
Tipus: Article
Altres publicacions en: Revista matemática iberoamericana
Resum
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.