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On the maximizing problem associated with critical Sobolev inequality under inhomogeneous constraints.
- Source :
- Complex Variables & Elliptic Equations; May2023, Vol. 68 Issue 5, p681-700, 20p
- Publication Year :
- 2023
-
Abstract
- In this paper, we study a maximizing problem associated with the critical Sobolev inequality under inhomogeneous constraints. The problem of this type was previously studied by Ishiwata and Wadade [On the effect of equivalent constrain on a maximizing problem associated with the Sobolev type embedding in R N . Math Ann. 2016;364:1043–1068; On the maximizing problem associated with Sobolev type embeddings under inhomogeneous constraints. Appl Anal. 2019;98(10):1916–1934], Ishiwata [On variational problems associated with Sobolev type inequalities and related topics. Available from: ] and Nguyen [Maximizers for the variational problems associated with Sobolev type inequalities under constraints. Math Ann. 2018;372(1–2):229–255]. Our results give a complete picture of the effect of the constraints on the attainability and non-attainability of the problem. The sharp Sobolev inequality plays a crucial role in our argument. Our method also provides a new and simple proof for the recent results of Ishiwata and Wadade [On the maximizing problem associated with Sobolev type embeddings under inhomogeneous constraints. Appl Anal. 2019;98(10):1916–1934] concerning the sub-critical Sobolev-type inequalities (or Gagliardo–Nirenberg inequalities). [ABSTRACT FROM AUTHOR]
- Subjects :
- MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 17476933
- Volume :
- 68
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Complex Variables & Elliptic Equations
- Publication Type :
- Academic Journal
- Accession number :
- 163446144
- Full Text :
- https://doi.org/10.1080/17476933.2021.1921751