2024/06/12 by Ignacio Ceresa Dussel, Dussel, Ignacio Ceresa
Engineering · Psychology · #Analysis of PDEs (math.AP) #Color perception and design #FOS: Mathematics #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2406.08579
openalex publication_date 2024/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this research, we investigate a general shape optimization problem in which the state equation is expressed using a nonlocal and nonlinear operator. We prove the existence of a minimum point for a functional F defined on the family of all 'quasi-open' subsets of a bounded open set Ω in ℝn. This is ensured under the condition that F demonstrates decreasing behavior concerning set inclusion and is lower semicontinuous with respect to a suitable topology associated with the fractional p-Laplacian under Dirichlet boundary conditions. Moreover, we study the asymptotic behavior of the solutions when s→1 and extend this result to the anisotropic case.