A control problem related to the parabolic dominative p-Laplace equation. (June 2020)

• Record Type: Journal Article
• Authors: Høeg, Fredrik Arbo; Ruosteenoja, Eero
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35K20 -- 91A22; Parabolic equations -- Dominative p-Laplacian -- Optimal control -- Viscosity solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111721
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We show that value functions of a certain time-dependent control problem in Ω × ( 0, T ), with a continuous payoff F on the parabolic boundary, converge uniformly to the viscosity solution of the parabolic dominative p -Laplace equation 2 ( n + p ) u t = Δ u + ( p − 2 ) λ n ( D 2 u ), with the boundary data F . Here 2 < p < ∞, and λ n ( D 2 u ) is the largest eigenvalue of the Hessian D 2 u .