Extremal functions for Trudinger-Moser inequalities of Adimurthi-Druet type in dimension two

By Y. Yang. 2015

115 citations recorded by the source corpus.

Combining Carleson-Chang's result with blow-up analysis, we prove existence of extremal functions for certain Trudinger-Moser inequalities in dimension two. This kind of inequality was originally proposed by Adimurthi and O. Druet, extended by the author to high dimensional case and Riemannian surface case, generalized by C. Tintarev to wider cases including singular form and by M. de Souza and J. M. do \'O to the whole Euclidean space R^2. In addition to the Euclidean case, we also consider the Riemannian surface case. The results in the current paper complement that of L. Carleson and A. Chang, M. Struwe, M. Flucher, K. Lin, and Adimurthi-Druet, our previous ones, and part of C. Tintarev.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/984cadefcd7b312ffdd826d58f9df89251236ae1

How researchers see this paper

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In Applied Mathematics

1. Xiaobao Zhu
2. Y. Yang
3. G. Lu
4. Nguyen Huong Lam
5. Caifeng Zhang
6. Federica Sani

In Computational Theory and Mathematics

1. Xiaobao Zhu
2. Y. Yang
3. G. Lu
4. Nguyen Huong Lam
5. Caifeng Zhang
6. Federica Sani

In Mathematical Physics

1. Xiaobao Zhu
2. Y. Yang
3. G. Lu

Citations in the corpus

• Blow-up analysis concerning singular Trudinger–Moser inequalities in dimension two (2016, methodology): “In a recent work [32], we generalized the inequality (4) to the case that large eigenvalues are involved, as well as to the manifold case.”