Report Title：k-QUASIMONOTONICITY AND UNIQUENESS FOR VARIATIONAL PROBLEMS IN NONTRIVIAL DOMAINS UNDER AFFINE BOUNDARY CONDITIONS (1-10)
Reporter：Professor Zhang Kewei
Affiliation: University of Nottingham（UK）
Report Time: 10:00-12:30, 14:00-17:30 May 19, 2026(lesson 1-6); 9:00-12:30 May 20, 2026 (lesson 7-10)
Report Location: Room 105, Zhengxin Building
University Contact: Wei Yuanhong (weiyuanhong@jlu.edu.cn)
Abstract:
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 Rnwith n > k ≥ 2. We present several examples of strictly regularly 1 and 2-quasimonotone functions defined in the matrix space M3×3and k-quasimonotone functions defined in more general MN×nwhich 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.
Bio:
Zhang Kewei is a professor at the University of Nottingham, UK. His research interests encompass variational methods, systems of partial differential equations, elasticity, and material microstructures. In recent years, his research interests have also included geometric singularity extraction, function approximation, image processing, and smooth optimization.
