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Comparison results for solutions of Poisson equations with Robin boundary on complete Riemannian manifolds.
- Source :
-
International Journal of Mathematics . Jul2023, Vol. 34 Issue 8, p1-19. 19p. - Publication Year :
- 2023
-
Abstract
- In this paper, by using Schwarz rearrangement and isoperimetric inequalities, we prove comparison results for the solutions of Poisson equations on complete Riemannian manifolds with Ric ≥ (n − 1) κ , κ = 0 or 1 , which extends the results in [A. Alvino, C. Nitsch and C. Trombetti, A Talenti comparison result for solutions to elliptic problems with Robin boundary conditions, Comm. Pure Appl. Math. 76(3) (2023) 585–603]. Furthermore, as applications of our comparison results, we obtain the Saint-Venant inequality and Bossel–Daners inequality for Robin Laplacian. [ABSTRACT FROM AUTHOR]
- Subjects :
- *RIEMANNIAN manifolds
*ISOPERIMETRIC inequalities
*EQUATIONS
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 0129167X
- Volume :
- 34
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- International Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 166743701
- Full Text :
- https://doi.org/10.1142/S0129167X23500453