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.
Open position: A three-month scholarship (PLN 4,600 per month) for a PhD student starting on 1 September 2026. For more details, see https://matinf.uj.edu.pl/konkursy/
Publications:
- G. Valette, On the Laplace equation on bounded subanalytic manifolds, Calculus of Variations and Partial Differential Equations vol. 63, (2024) article no. 236
- 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 vol. 390 (2024), 2413–2457
- B. Kocel-Cynk, W. Pawłucki & A. Valette, Semialgebraic Calderón-Zygmund theorem on regularization of the distance function, Mathematische Annalen vol. 390 (2024), 1863–1883
- 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, Sobolev embedding theorem and subanalytic measures
- B. Kocel-Cynk, W. Pawłucki & A. Valette, A simplified proof of the o-minimal Whitney extension theorem (to be published in Studia Mathematica)
- Nhan Nguyen, A. Valette & G. Valette, Inner Lipschitz approximation in o-minimal structures
- G. Valette, Density of Neumann regular smooth functions in Sobolev spaces of subanalytic manifolds
- G. Valette, Lp Hodge theory for bounded subanalytic manifolds
- G. Valette, W1,p a priori estimates for solutions of linear elliptic PDEs on subanalytic domains
