Abstract
In this paper we provide a comparison result between the solutions to the torsion problem for the Hermite operator with Robin boundary conditions and the one of a suitable symmetrized problem.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Availability of data and material
Not applicable.
Code Availability
Not applicable.
Change history
23 July 2022
Missing Open Access funding information has been added in the Funding Note.
References
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. on Pure and Applied Math.
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)
Bogachev, V.I.: Gaussian Measures Mathematical Surveys and Monographs, vol. 62. American Mathematical Society, Providence (1998)
Byron, F.W., Fuller, R.W.: Mathematics of Classical and Quantum Physics. Dover Publications, Inc., New York (1992)
Borell, C.: The Brunn-Minkowski inequality in Gauss space. Invent. Math. 30, 207–216 (1975)
Bucur, D., Giacomini, A.: The Saint-Venant inequality for the Laplace operator with Robin boundary conditions. Milan J. Math. 83(2), 327–343 (2015)
Carlen, E.A., Kerce, C.: On the cases of equality in Bobkov’s inequality and Gaussian rearrangement. Calc. Var. Partial Diff. Equ. 13, 1–18 (2001)
Cianchi, A., Fusco, N., Maggi, F., Pratelli, A.: On the isoperimetric deficit in Gauss space. Amer. J. Math. 133(1), 131–186 (2011)
Chiacchio, F., Gavitone, N.: The Faber-Krahn inequality for the Hermite operator with Robin boundary conditions, Math Annalen (in press)
Ehrhard, A.: Eléments extremaux pour les inégalités de Brunn-Minkowski gaussennes. Ann. Inst. H. Poincaré, Anal. Non Linéaire 22, 149–168 (1986)
Sudakov, V.N., Cirel’son, B.S.: Extremal properties of half-spaces for spherically invariant measures, Extremal properties of half-spaces for spherically invariant measures (Russian). Problems in theTheory of Probability Distributions, II. Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 41 14–24, 165 (1974)
Funding
Open access funding provided by Università degli Studi di Napoli Federico II within the CRUI-CARE Agreement. This work has been partially supported by the PRIN project 2017JPCAPN (Italy) grant: “Qualitative and quantitative aspects of nonlinear PDEs”, by FRA 2020 “Optimization problems in Geometric-functional inequalities and nonlinear PDE’s” (OPtImIzE) and by GNAMPA of INdAM.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
On behalf of all authors, the corresponding author declares that there are no financial or non-financial interests that are directly or indirectly related to the work submitted for publication.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Chiacchio, F., Gavitone, N., Nitsch, C. et al. Sharp Estimates for the Gaussian Torsional Rigidity with Robin Boundary Conditions. Potential Anal 59, 1107–1116 (2023). https://doi.org/10.1007/s11118-022-09995-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11118-022-09995-8