Weighted symmetrization results for a problem with variable Robin parameter

Author:

Alvino Angelo,Chiacchio Francesco,Nitsch Carlo,Trombetti Cristina

Abstract

AbstractBy means of a suitable weighted rearrangement, we obtain various apriori bounds for the solutions to a Robin problem. Among other things, we derive a family of Faber-Krahn type inequalities.

Funder

Università degli Studi di Napoli Federico II

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics

Reference24 articles.

1. Adams, R.: Sobolev Spaces. Elsevier, Oxford (2003)

2. Alvino, A., Chiacchio, F., Nitsch, C., Trombetti, C.: Sharp estimates for solutions to elliptic problems with mixed boundary conditions. J. Math. Pures Appl. 9(152), 251–261 (2021)

3. Alvino, A., Brock, F., Chiacchio, F., Mercaldo, A., Posteraro, M.R.: Some isoperimetric inequalities on $$\mathbb{R} ^{N}$$ with respect to weights $$\left|x\right|^{\alpha }$$. J. Math. Anal. Appl. 451(1), 280–318 (2017)

4. Alvino, A., Trombetti, G., Matarasso, S.: Elliptic boundary value problems: comparison results via symmetrization. Ricerche Mat. 51(2), 341–355 (2003)

5. Alvino, A., Nitsch, C., Trombetti, C.: A Talenti comparison result for solutions to elliptic problems with Robin boundary conditions, arXiv:1909.11950, to appear on Comm. Pure Applied Math

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