Minimizing Sequences of Sobolev Inequalities Revisited
Abstract We give a new proof of the compactness of minimizing sequences of the Sobolev inequalities in the critical case. Our approach relies on a simplified version of the concentration-compactness principle, which does not require any refinement of the Sobolev embedding theorem.
Authors
- Phan Thành Nam (ORCID: https://orcid.org/0000-0001-7599-9742)
- Charlotte Dietze (ORCID: https://orcid.org/0000-0002-7111-1467)
Institutions
- LMU Klinikum (DE)
- Munich Center for Quantum Science and Technology (DE)
- Ludwig-Maximilians-Universität München (DE)
- Institut des Hautes Études Scientifiques (FR)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2025-06-30
- DOI
- https://doi.org/10.1093/imrn/rnaf190
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 0.00