On the equation DutHDu=G. (January 2022)

• Record Type: Journal Article
• Authors: Bandyopadhyay, S.; Dacorogna, B.; Matveev, V.; Troyanov, M.
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: Pullback equation -- Dirichlet problem -- Dirichlet–Neumann problem; 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.2021.112554
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this article, we want to find a map u : Ω ¯ → R n solving, in Ω, the equation u ∗ H = G i . e . D u t H u D u = G and coupled, on ∂ Ω, either with the Dirichlet–Neumann problem u = φ and D u = D φ or the purely Dirichlet problem u = φ where Ω ⊂ R n is a bounded open set, G, H : R n → R n × n and φ : Ω ¯ → R n are given. We discuss the case where G and H are not necessarily symmetric or skew-symmetric, but have invertible symmetric parts.