课程题目：k-QUASIMONOTONICITY AND UNIQUENESS FOR VARIATIONAL PROBLEMS IN NONTRIVIAL DOMAINS UNDER AFFINE BOUNDARY CONDITIONS (1-10)

报告人：Zhang Kewei 教授

所在单位：University of Nottingham （UK）

报告时间：2026年5月19日 10:00-12:30; 14:00-17:30 (lesson 1-6）

          2026年5月20日 9:00-12:30 (lesson 7-10）

报告地点：正新楼105室

校内联系人：魏元鸿 [email protected]

课程摘要：

We establish a uniqueness result for smooth solutions of nonlinear variational problems with affine boundary conditions motivated from nonlinear elasticity in certain non-starshaped or topologically non-trivial k-starshaped domains under the strictly regular k-quasimonotonicity conditions for the integrands. Examples of non-trivial domains we consider include non-starshaped cylindrical domains which are 1-starshaped and some tubular neighbourhoods of k-dimensional domains in Rⁿ with n > k ≥ 2. We present several examples of strictly regularly 1 and 2-quasimonotone functions defined in the matrix space M^3×3 and k-quasimonotone functions defined in more general M^N×n which are polyconvex but their gradients are not quasimonotone. These models can either be coercive or non-coercive. The notion of strict regular k-quasimonotonicity fills the gaps between quasiconvexity where k = 0 and uniqueness results hold on starshaped domains, and gradient quasimonotone mappings where k = n and uniqueness is independent of geometry or topology of domain.

报告人简介：

张克威，英国诺丁汉大学教授。研究兴趣包括变分法，偏微分方程组，弹性力学，材料微结构等。近年研究兴趣包括几何奇点提取，函数逼近，图像处理，光滑优化等。