Geometric Analysis
Main funder
Funder's project number: 323960
Funds granted by main funder (€)
- 600 000,00
Funding program
Project timetable
Project start date: 01/09/2019
Project end date: 31/08/2023
Summary
The project deals with Sobolev spaces, Sobolev mappings, regularity theory and geometry of domains. Geometric criteria for the
possibility to extend Sobolev functions defined on a given domain to the corresponding Sobolev space over the underlying Euclidean
space are investigated. Functional properties of the validity of such an extension will be established. Trace theorems and invariance
properties of function spaces under composition operators will be given. For Sobolev mappings, one studies existence, regularity and
topological properties. One further studies regularity problems for harmonic functions and other related solutions under curvature
assumptions on the underlying space.
possibility to extend Sobolev functions defined on a given domain to the corresponding Sobolev space over the underlying Euclidean
space are investigated. Functional properties of the validity of such an extension will be established. Trace theorems and invariance
properties of function spaces under composition operators will be given. For Sobolev mappings, one studies existence, regularity and
topological properties. One further studies regularity problems for harmonic functions and other related solutions under curvature
assumptions on the underlying space.
Principal Investigator
Primary responsible unit
Related publications and other outputs
1 of 2
- Bourgain-Brezis-Mironescu formula for Ws,p q -spaces in arbitrary domains (2024) Mohanta, Kaushik; A1; OA
- Existence of quasiconformal mappings in a given Hardy space (2024) Bouchala, Ondřej; et al.; A1
- Magnetic fractional Poincaré inequality in punctured domains (2024) Bal, Kaushik; et al.; A1; OA
- Sobolev Extensions over Cantor-Cuspidal Graphs (2024) Koskela, Pekka; et al.; A1; OA
- Existence and uniqueness of limits at infinity for homogeneous Sobolev functions (2023) Koskela, Pekka; et al.; A1; OA
- Bi-Lipschitz invariance of planar BV- and W1,1-extension domains (2022) García-Bravo, Miguel; et al.; A1; OA
- On Limits at Infinity of Weighted Sobolev Functions (2022) Eriksson-Bique, Sylvester; et al.; A1; OA
- Pointwise inequalities for Sobolev functions on generalized cuspidal domains (2022) Zhu, Zheng; A1; OA
- Sobolev Extensions Via Reflections (2022) Koskela, P.; et al.; A1; OA
- The volume of the boundary of a Sobolev (p,q)-extension domain (2022) Koskela, Pekka; et al.; A1; OA
