NCN Opus 22 2021/43/B/ST1/02359
Partial differential equations on subanalytic domains and manifolds
The aim of the project is to carry out the theory of elliptic partial differential equations on any subanalytic domain, with possibly non Lipschitz boundary. This involves to carry out a complete theory of Sobolev spaces of subanalytic domains.
Publications:
- A. Valette & G. Valette, Trace operators on bounded subanalytic manifolds, Selecta Mathematica vol. 30, 54 (2024)
- G. Valette, On Sobolev spaces of bounded subanalytic manifolds, Mathematische Annalen (2024) (arXiv)
- B. Kocel-Cynk, W. Pawłucki & A. Valette, Semialgebraic Calderón-Zygmund theorem on regularization of the distance function, Mathematische Annalen (2024)
- G. Valette, Regular Vectors and Bi-Lipschitz Trivial Stratifications in O-Minimal Structures, in "Handbook of Geometry and Topology of Singularities IV", Springer (2023)
- A. Valette & G. Valette, A remark on C∞ definable equivalence, Annales Polonici Mathematici vol. 131.1 (2023), 79-84
- A. Valette & G. Valette, Uniform Poincare inequality in o-minimal structures, Mathematical Inequalities and Applications vol. 26 (2023), 141-150
Preprints:
- G. Valette, On the Laplace equation on bounded subanalytic manifolds
- G. Valette, Lp Hodge theory for bounded subanalytic manifolds
Open position:
There is a 2 years position for a PhD student starting from October 2024.
Announcement, deadline for applications: September 16, 2024.
