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

• Pascal Auscher ^[1] ; Mihalis Mourgoglou ^[2]
  1. [1] University of Picardie Jules Verne

     University of Picardie Jules Verne

     Arrondissement d’Amiens, Francia

     
  2. [2] Universidad del País Vasco/Euskal Herriko Unibertsitatea

     Universidad del País Vasco/Euskal Herriko Unibertsitatea

     Leioa, España

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 1, 2019, págs. 241-315
• Idioma: inglés
• DOI: 10.4171/rmi/1054
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.