走向现代数学学术报告 - 杜力力教授（No. 971)

报告题目：The regularity of free boundary for a highly singular obstacle-type problem

报 告 人：杜力力 教授（四川大学）

邀 请 人：李心亮 博士

报告时间：2026年10月15日 15：10

报告地点：东海岸校区D209

报告摘要：In recent work, Allen, Kriventsov and Shahgholian [J. Lond. Math. Soc. 2025] studied the regularity of the free boundary for the semilinear obstacle-type problem

under structural assumptions on f, including, for 0 < t ≤ 1,

.

They left open whether free boundary regularity still holds for . In this talk, we will introduce our recent work, which gives a partial affirmative answer by studying

More precisely, we obtain the desired regularity conclusion over the full range through a detailed analysis of blow-up limits. We prove that every blow-up limit is homogeneous of degree , and the free boundary is locally the graph of a function near regular points for some .

报告人简介：杜力力，四川大学数学学院教授、博士生导师，国家青年基金A类（原国家杰出青年基金）、国家优秀青年基金获得者、教育部青年长江学者、四川省学术和技术带头人，在Arch. Rational Mech. Anal., Math. Ann., Comm. Math. Phys., Tran. AMS., Comm. PDEs，Calculus of Variations and PDEs等国际数学期刊发表学术论文50余篇，先后主持国家自然科学基金项目6项、省部级项目多项。