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arXiv · 2306.08639

Souplet-Zhang and Hamilton type gradient estimates for nonlinear elliptic equations on smooth metric measure spaces

Ali Taheri·Vahideh Vahidifar
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Abstract

In this article we present new gradient estimates for positive solutions to a class of nonlinear elliptic equations involving the f-Laplacian on a smooth metric measure space. The gradient estimates of interest are of Souplet-Zhang and Hamilton types respectively and are established under natural lower bounds on the generalised Bakry-Émery Ricci curvature tensor. From these estimates we derive amongst other things Harnack inequalities and general global constancy and Liouville-type theorems. The results and approach undertaken here provide a unified treatment and extend and improve various existing results in the literature. Some implications and applications are presented and discussed.

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Ali Taheri, Vahideh Vahidifar. 2023-06-14. Souplet-Zhang and Hamilton type gradient estimates for nonlinear elliptic equations on smooth metric measure spaces. https://arxiv.org/abs/2306.08639

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