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- Title
Sharp affine weighted L<sup>2</sup> Sobolev inequalities on the upper half space.
- Authors
Dou, Jingbo; Hu, Yunyun; Yue, Caihui
- Abstract
We establish some sharp affine weighted L2 Sobolev inequalities on the upper half space, which involves a divergent operator with degeneracy on the boundary. Moreover, for some certain exponents cases, we also characterize the extremal functions and best constants. Our approach only relies on the L2 structure of gradient norm, affine invariance and a class of weighted L2 Sobolev inequality on the upper half space. This is a simple approach which does not depend on the geometric structure of Euclidean space such as Brunn–Minkowski theory on convex geometry.
- Subjects
CONVEX geometry; EXPONENTS
- Publication
Advanced Nonlinear Studies, 2024, Vol 24, Issue 2, p415
- ISSN
1536-1365
- Publication type
Article
- DOI
10.1515/ans-2023-0117