报告人：Professor Jie Xiao (加拿大纽芬兰纪念大学）

时间： 2024年08月31日、9月1日、9月2日上午， 9:00-11:00

地点：国学馆110

1.Hypersurface potentials & capacities via semilinear wave equations

摘要: Based on the paper joint with David R. Adams entitled above, this talk will demonstrate a case study of: not only the newly-discovered hypersurface potential & hypersurface capacity living on a homogeneous graph; but also the induced wave potential under the spherical symmetry with respect to the space variable; as well as a unique weak solution of the model semilinear wave equation.

2. Full capacity-volumetry of sharp exp-integrability law

摘要: Based on the paper joint with David R. Adams entitled above, this talk will use Law of Trichotomy to show a full range of capacity-volumetry of the sharp exp-integrability law which covers the sharp Adams-Moser-Trudinger exp-integrability law for higher order derivatives, thereby discovering a new approach to a relatively complete family of the essential capacity-volumetric estimates with optimal constants including the sharp Ahlfors-Beurling-P& Morrey-Sobolev capacity-volumetric inequalities.

3. A geometric measure theoretic look at the Besov capacities

摘要: Based on the paper joint with David R. Adams entitled above, this talk will present not only a capacitary variant of the homogeneous Besov exp-integrability but also an extension of the Choquet-Hausdorff integration of the Hardy-Littlewood maximal operator through a dyadic Hausdroff-Netrusov capacity which actually amounts to a nonhomogeneous Besov capacity.

专家简介: 肖杰教授的研究和教学兴趣在于几何分析和偏微分方程。特别地，肖杰教授致力于调和分析，复分析和算子理论及其交叉应用，但也将函数空间和位势理论的方法和技术应用于共形微分几何、热方程、纳维-斯托克斯方程和波动方程的研究。迄今为止，肖杰教授有200多篇文章发表在国际领先的数学期刊上，包括《Adv. Math.》、《J. Math. Pures Appl.》、《J. Eur. Math. Soc》等。 同时，肖杰教授已发表6本教材和专著。此外，肖杰教授还担任《Advances in Analysis and Geometry》和《Canadian Mathematical Bulleti》期刊的主编，以及《Journal of Mathematical Analysis and Applications》的部门编辑。