A Note About a Caffarelli-Kohn-Nirenberg Type Inequality for Euclidean Submanifolds

被引：0

作者：

Batista, M. ^{[1
]}

Mirandola, H. ^{[2
]}

Vitorio, F. ^{[1
]}

机构：

[1] Univ Fed Alagoas, CPMAT IM, BR-57072970 Maceio, AL, Brazil

[2] Univ Fed Rio de Janeiro, Inst Matemat, BR-21945970 Rio De Janeiro, RJ, Brazil

来源：

RESULTS IN MATHEMATICS | 2023年 / 78卷 / 03期

关键词：

Hardy-Sobolev inequalities; interpolation; submanifolds; Gagliardo-Nirenberg inequality; NONNEGATIVE RICCI CURVATURE; ISOPERIMETRIC-INEQUALITIES; SOBOLEV; MANIFOLDS;

D O I：

10.1007/s00025-023-01892-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the seminal paper, Michael and Simon (Comm Pure Appl Math 26:361-379, 1973) generalized the celebrated Sobolev inequality for submanifolds into Euclidean spaces. The universal constant obtained by them does not depend on the submanifold. A sort of applications to the submanifold theory can be derived from that inequality. Batista et al. (J Differ Equ 263:5813-5829, 2017) the authors proved an optimal Hardy-Sobolev inequality for Euclidean submanifolds, in the same vein as Carron (J Math Pures Appl 76(10):883-891, 1997). In this paper, we prove a weighted Michael-Simon-Sobolev and a Caffarelli-Kohn-Nirenberg inequality, as well as some of their derivatives, such as Gagliardo-Nirenberg and Nash inequalities, for submanifolds in Euclidean spaces.

引用

页数：15

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