Weighted critical exponents of Sobolev-type embeddings for radial functions

Author:

Su Jiabao1,Wang Cong1

Affiliation:

1. School of Mathematical Sciences, Capital Normal University , Beijing 100048 , People’s Republic of China

Abstract

Abstract In this article, we prove the upper weighted critical exponents for some embeddings from weighted Sobolev spaces of radial functions into weighted Lebesgue spaces. We also consider the lower critical exponent for certain embedding.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Reference20 articles.

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2. J. Byeon and Z.-Q. Wang, Symmetry breaking of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities. Commun. Contemp. Math. 4 (2002), 457–465.

3. L. Caffarelli, R. Kohn, and L. Nirenberg, First order interpolation inequalities with weights. Compositio Math. 53 (1984)259–275.

4. F. Catrina and Z.-Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions, Comm. Pure Appl. Math. 54 (2001), 229–258.

5. F. Catrina and Z.-Q. Wang, A one-dimensional nonlinear degenerate elliptic equation, Proceedings of the USA-Chile Workshop on Nonlinear Analysis (Viña del Mar-Valparaiso, 2000), Electron. J. Differ. Equ. Conf., 6, Southwest Texas State University, San Marcos, TX, 2001.

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