On the equation DutHDu=G. (January 2022) - Bandyopadhyay, S.; Dacorogna, B.; Matveev, V.; Troyanov, M.
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.