Semilinear equations with integral bounded Ricci curvature

发布时间：2025-12-15 来源：william威廉亚洲浏览次数：

Speaker:	魏国栋	DateTime:	2025年12月16日（周二）下午16:30-17:30
Brief Introduction to Speaker: 魏国栋，中山大学。		Place:	国交2号楼315会议室
Abstract:In 1981, Gidas and Spruck established the celebrated Liouville property for the semilinear equation when defined on a Riemannian manifolds with nonnegative Ricci curvature. In this talk, I will focus on the Liouville property and local behavior of such type semilinear equations (include p-Laplacian equations) with integral bounded Ricci curvature. We will show that the Liouville property still holds when \\|Ric_\\|_q is less than a certain multiple of the Sobolev constant. As an application, we provide a “one end” criterion in the case of small \\|Ric_\\|_q. This can be somehow regarded as an integral verson of the end estimate due to Cai, Colding and Yang. Furthermore, by applying the Nash-Moser iteration, we derive a local gradient estimate for this class of equations in terms of the intergral Ricci curvature bound. This result particularly improves the work due to Peterson and Wei. This talk is based on joint work with Prof. Youde Wang and Liqin Zhang.