On two thermal insulation problems

发布时间：2022-03-21 作者：77779193永利官网浏览次数：

Speaker:	李沁峰	DateTime:	2022年03月18日（周五） 9:30-11:30
Brief Introduction to Speaker: 李沁峰，湖南大学副教授，主要研究偏微分方程，主要关注几何变分问题以及几何测度论在其中的应用，和半线性椭圆方程。在本领域做出了很好的工作，部分成果发表在Indiana Univ. Math. J. 、 Int. Math. Res. Not. IMRN 、 Calc. Var. Partial Differential Equations等知名期刊上。		Place:	腾讯会议：987-109-143
Abstract: In this talk, I will introduce my recent works joint with Hengrong Du, Yong Huang, Qiuqi Li and Changyou Wang on two optimization problems from thermal insulation background. For fixed Lipschitz domain setting aimed at finding optimal insulation of material, we prove global $W^{1,p}$ and Holder estimate for minimizers, and thus obtain concentration breaking phenomena of insulation material for both problems. We also obtain exact value of breaking thresholds. Considering varying domains aimed at designing optimal shape, we prove compactness of a class of Sobolev extension domains, uniform Poincare inequality and existence of optimal shapes. We also carry on stability analysis in both problems, and discuss optimality of ball shape among regions with prescribed volume.