| Autor: |
Alvino, A., Brock, F., Chiacchio, F., Mercaldo, A., Posteraro, M. R. |
| Rok vydání: |
2016 |
| Předmět: |
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| DOI: |
10.48550/arxiv.1606.02195 |
| Popis: |
We solve a class of isoperimetric problems on $\mathbb{R}^N $ with respect to weights that are powers of the distance to the origin. For instance we show that if $k\in [0,1]$, then among all smooth sets $��$ in $\mathbb{R} ^N$ with fixed Lebesgue measure, $\int_{\partial ��} |x|^k \, \mathscr{H}_{N-1} (dx)$ achieves its minimum for a ball centered at the origin. Our results also imply a weighted Polya-Sz��go 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. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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