Gradient estimates for nonlinear elliptic equations involving the Witten Laplacian on smooth metric measure spaces and implications-Reference-Cited by-同舟云学术

Gradient estimates for nonlinear elliptic equations involving the Witten Laplacian on smooth metric measure spaces and implications

Published:2023-01-01 Issue:1 Volume:12 Page:
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Taheri Ali¹,Vahidifar Vahideh¹

Affiliation:

1. School of Mathematical and Physical Sciences, University of Sussex, Falmer , Brighton , United Kingdom

Abstract

AbstractThis article presents new local and global gradient estimates of Li-Yau type for positive solutions to a class of nonlinear elliptic equations on smooth metric measure spaces involving the Witten Laplacian. The estimates are derived under natural lower bounds on the associated Bakry-Émery Ricci curvature tensor and find utility in proving fairly general Harnack inequalities and Liouville-type theorems to name a few. The results here unify, extend and improve various existing results in the literature for special nonlinearities already of huge interest and applications. Some consequences are presented and discussed.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anona-2022-0288/pdf

Reference54 articles.

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3. D. Bakry and M. Émery, Diffusions hypercontractives, In: J. Azḿa, M. Yor, eds, Séminaire de Probabilités XIX 1983/84. Lecture Notes in Mathematics, vol. 1123, Springer, Berlin, Heidelberg.

4. D. Bakry, I. Gentil, and M. Ledoux, Analysis and geometry of Markov diffusion operators, A Series of Comprehensive Studies in Mathematics, vol. 348, Springer, 2012.

5. M. F. Biduat-Vèron and L. Veròn, Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of the Emden equations, Invent. Math. 106 (1991), 489–539.

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