2025/12/15 by M. H. M. Rashid, Rashid, M. H. M.
Computer Science · Engineering · #35J87 #47J20 #49J40 #65K15 #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2512.13275
openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28
This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of operators converge pointwise while preserving fundamental properties including homogeneity, strong monotonicity, Lipschitz continuity, and T-monotonicity. Our analysis extends to regularization techniques, finite-dimensional approximations, and non-monotone nonlinearities, providing explicit convergence rates under appropriate conditions. The theory encompasses applications to p-Laplacian operators, elliptic regularizations, and optimal control problems with QVI constraints. By developing a unified framework that bridges classical monotone operator theory with contemporary computational challenges, this work provides essential mathematical foundations for the robust numerical approximation and sensitivity analysis of quasi-variational problems arising in materials science, physics, and engineering applications.