Sharp affine weighted <i>L</i> <sup>2</sup> Sobolev inequalities on the upper half space-Reference-Cited by-同舟云学术

Sharp affine weighted L ² Sobolev inequalities on the upper half space

Published:2024-03-14 Issue:2 Volume:24 Page:415-435
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Dou Jingbo¹,Hu Yunyun¹,Yue Caihui¹

Affiliation:

1. School of Mathematics and Statistics , Shaanxi Normal University , Xi’an , Shaanxi , 710119 , China

Abstract

Abstract We establish some sharp affine weighted L 2 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 L 2 structure of gradient norm, affine invariance and a class of weighted L 2 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.

Funder

National Natural Science Foundation of China

Youth Innovation Team of Shaanxi Universities

Fundamental Research Funds for the Central Universities

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/ans-2023-0117/pdf

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