Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775035 | Journal of Mathematical Analysis and Applications | 2017 | 42 Pages |
Abstract
We solve a class of isoperimetric problems on RN with respect to weights that are powers of the distance to the origin. For instance we show that, if kâ[0,1], then among all smooth sets Ω in RN with fixed Lebesgue measure, â«âΩ|x|kHNâ1(dx) achieves its minimum for a ball centered at the origin. Our results also imply a weighted Pólya-Szegö principle. In turn, we establish radiality of optimizers in some Caffarelli-Kohn-Nirenberg inequalities, and we obtain sharp bounds for eigenvalues of some nonlinear problems.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
A. Alvino, F. Brock, F. Chiacchio, A. Mercaldo, M.R. Posteraro,