自由边界调和映射的抛物型缺陷测度

中文摘要 AI 辅助

我们针对一类具有自由边界的调和映射的热流引入了缺陷测度，并启动了对其的分析。我们的热流受域边界上奇异摄动的启发，强调了具有自由边界的调和映射与其经典对应物之间的结构差异。我们考虑的调和映射是Da Lio和Rivière引入的映射的重新表述，并出现在Steklov特征值的谱几何的若干问题中。与经典情形相反，我们考虑的热流表现出全局性质的特征，并且爆破分析变得更加具有挑战性。

英文摘要

We introduce defect measures for the heat flow of a class of harmonic maps with free boundary and initiate their analysis. Our flow is motivated by singular perturbations on the boundary of the domain, emphasizing structural differences between harmonic maps with free boundary and their classical counterpart. The harmonic maps we consider are a reformulation of maps introduced by Da Lio and Rivière and arise in several problems in the spectral geometry of Steklov eigenvalues. Contrary to the classical case, the flow we consider exhibits features of global nature and the blow-up analysis turns out to be much more challenging.

发表机构

• Tata Institute of Fundamental Research（塔塔基础研究所）
• Johns Hopkins University（约翰斯·霍普金斯大学）

机构由 AI 辅助整理，请以论文原文为准。