﻿ Direct methods on non-local operators and symmetry of solutions for equations with fractional p-Laplacians -大连理工大学数学科学学院（新）

# Direct methods on non-local operators and symmetry of solutions for equations with fractional p-Laplacians

2017年07月08日 13:41  点击：[]

学术报告

报告题目：Direct methods on non-local operators and symmetry of solutions for equations with fractional p-Laplacians

报告人：陈文雄  教授

报告校内联系人：李风泉 教授

联系方式：84708351-8124

报告时间：2017711日下午1530-1630

报告地点：创新园大厦A1101

报告摘要：In this talk, we will first give a survey on the direct methods we introduced in recent years to study nonlinear equations involving pseudo-differential nonlocal operators, such as the direct method of moving planes, moving spheres, and blowing-up and re-scaling. Then we will focus on nonlinear equations involving the fractional p-Laplacian. We prove a maximum principle for anti-symmetric functions and obtain other key ingredients for carrying on the method of moving planes, such as a key boundary estimate lemma. Then we establish radial symmetry and monotonicity for positive solutions to semi-linear equations involving the fractional p-Laplacian in a unit ball and in the whole space. We believe that the methods developed here can be applied to a variety of problems involving nonlinear nonlocal operators.

报告人简介：文雄，美国纽约Yeshiva 大学终身教授，数学系主任，西北工业大学特聘讲座教授，国际知名的数学家。曾多次获得美国国家科学基奖。担任Nonlinear Analysis: Theory, Methods & Applications Communications on Pure and Applied Analysis 两个SCI 数学杂志的编辑。

研究方向:非线性偏微分方程

研究成果主要发表在Annals of Math, J. of Diff. Geom, Comm. Pure and Appl. Math, Duke Math. J, Advances in Math,Trans. AMS等国际一流期刊上，其中1991 发表在Duke Math. J.上的文章已被引用500余次, 2006 发表在CPAM 的文章已被引高达400 次以上,近年来，他在Advances in Mathematics 发表的文章中有三篇被列为被引Highly Cited)

数学科学学院

201777

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