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Sharp anisotropic singular Trudinger–Moser inequalities in the entire space.
- Source :
-
Calculus of Variations & Partial Differential Equations . May2024, Vol. 63 Issue 4, p1-24. 24p. - Publication Year :
- 2024
-
Abstract
- In this paper, we investigate sharp singular Trudinger–Moser inequalities involving the anisotropic Dirichlet norm ∫ R N F N (∇ u) d x 1 N in Sobolev-type space D N , q (R N) , N ≥ 2 , q ≥ 1 . Here F : R N → [ 0 , + ∞) is a convex function of class C 2 (R N \ { 0 }) , which is even and positively homogeneous of degree 1. Combing with the connection between convex symmetrization and Schwarz symmetrization, we will establish anisotropic singular Trudinger–Moser inequalities and discuss their sharpness under different situations, including the case ‖ F (∇ u) ‖ N ≤ 1 , the case ‖ F (∇ u) ‖ N a + ‖ u ‖ q b ≤ 1 , and whether they are associated with exact growth. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CONVEX functions
Subjects
Details
- Language :
- English
- ISSN :
- 09442669
- Volume :
- 63
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Calculus of Variations & Partial Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 177350171
- Full Text :
- https://doi.org/10.1007/s00526-024-02700-0