学术报告会：Dirichlet Boundary Value Problem for Degenerate Elliptic Equations

报告题目：Dirichlet Boundary Value Problem for Degenerate Elliptic Equations

报 告 人： 陈  化     (武汉大学    教授)

报告时间：2026年5月6日周三10：40

报告地点： S3-313

Abstract：In this talk, we introduce the background and properties of Hormander vector fields and present relevant research results for a class of subelliptic Dirichlet boundary value problems. For the subcritical growth case, we propose two distinct sufficient conditions for the multiplicity of weak solutions and sign-changing solutions, respectively. Our findings reveal that these two conditions each have their own advantages in different degenerate cases. Our latest research findings indicate that for the boundary value problems of degenerate elliptic equations, there are essential differences in the study of the existence of solutions compared to those of classical elliptic equations. This aspect depends on whether the degeneracy points of the operators are regular or singular.

      Furthermore, we discuss quasilinear subelliptic boundary value problems of the Baouendi-Grushin type with critical growth, establishing existence and regularity results for non-negative solutions and for positive solutions to Brezis-Nirenberg type problems.

个人简介：

陈化，武汉大学数学与统计学院教授，博士生导师，国家杰出青年科学基金获得者，国务院学科数学评议组第六届和第七届成员，教育部科技委第三届委员会委员。现为武汉大学数学协同创新中心主任，湖北省数学会理事长。研究方向为偏微分方程的微局部分析理论，退化型偏微分方程，具有生物和医学背景的偏微分方程和偏微分方程的谱理论；至今已主持多项国家自然科学基金重点项目，曾为国家重大项目973核心数学项目组成员（2001-2006）并获教育部跨世纪优秀人才基金 （1998-2000）。至今在国际上专业的SCI数学杂志上发表论文120多篇，曾获教育部科技进步奖二等奖两次，2017年主持的科研项目获得教育部自然科学奖一等奖。