2025.11.27 14:30--15:20 报告一: Introduction to the fractional elliptic and parabolic equations

报告简介：In this talk, I will introduce basic notions for fractional nonlocal elliptic and parabolic equations, including several equivalent definitions of the fractional Laplacian, the associated function spaces, and fundamental tools such as comparison principles. I will then present typical linear and semilinear models, and explain how nonlocality influences regularity and qualitative properties of solutions.

2025.11.27 15:30--16:20 报告二: Schauder regularity for fractional equations and applications

报告简介：This talk focuses on refined Schauder-type regularity for fractional elliptic equations and its applications. I will present local Hölder and $C^{k}$-regularity estimates for solutions of fractional Poisson equations, emphasizing that local information on the solution and the right-hand side is sufficient to control higher-order derivatives. Then, I will show how these estimates yield singularity and decay results for superlinear nonlocal problems in unbounded domains, such as fractional Lane–Emden type equations.

报告地点：腾讯会议 518-633-058  

报告人简介：武乐云，华南理工大学教授，博士生导师，广东省自然科学基金杰出青年项目获得者。主要从事非线性偏微分方程及其应用、反常扩散模型、生物趋向性运动模型的数学理论的研究。在 Adv. Math.，Calc. Var. Partial Differential Equations，SIAM J. Math. Anal.，Math. Z.，J. Differential Equations 等杂志发表论文20多篇。主持国家自然科学基金青年基金等多项项目。