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

By P. Auscher, Mihalis Mourgoglou. Revista matemática iberoamericana, 2014

67 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/332929bc67ab03ba5787a01953e069b84f71497d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Dachun Yang
2. Wen Yuan
3. Yangyang Zhang
4. Songbai Wang
5. Yoshihiro Sawano
6. Jun Liu
7. Ciqiang Zhuo
8. Yuan Zhou

In Control and Systems Engineering

1. Wen Yuan
2. Dachun Yang
3. Yangyang Zhang
4. Songbai Wang

In Mathematical Physics

1. Dachun Yang
2. Wen Yuan
3. Yangyang Zhang
4. Songbai Wang
5. Yoshihiro Sawano
6. Ciqiang Zhuo
7. Jun Liu
8. Xianjie Yan

Citations in the corpus

• Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces II: Littlewood–Paley Characterizations and Real Interpolation (2019, methodology): “Recall that the Orlicz-slice space (E Φ )t(R ) introduced in [81] generalizes both the slice space E p t (R ) [in this case, Φ(τ) := τ(2) for any τ ∈ [0,∞)], which was originally introduced by Auscher and Mourgoglou [8] and has been applied to study the”