2016/12/24 by Harbir Antil, Antil, Harbir, Mahamadi Warma +1
Computer Science · Mathematics · #35R11 #49J20 #49J45 #93C73 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1612.08201
openalex publication_date 2016/12/24 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28
In this paper we study optimal control problems with either fractional or regional fractional p-Laplace equation, of order s and p∈ [2,∞), as constraints over a bounded open set with Lipschitz continuous boundary. The control, which fulfills the pointwise box constraints, is given by the coefficient of the involved operator. To overcome the degeneracy of both fractional p-Laplacians, we introduce a regularization for both operators. We show existence and uniqueness of solution to the regularized state equations and existence of solution to the regularized optimal control problems. We also prove several auxiliary results for the regularized problems which are of independent interest. We conclude with the convergence of the regularized solutions.