Global existence of solutions to parabolic Monge–Ampère equations on Riemannian manifolds. (April 2015)

• Record Type: Journal Article
• Authors: Ru, Qiang
• Is Part Of: Nonlinear analysis. Volume 116(2015)
• Page Start: 145
• Page End: 152
• Publication Date: 2015-04
• Subjects: Global existence -- Monge–Ampère equation -- Riemannian manifold; 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.2014.12.025
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the Cauchy problem of the parabolic Monge–Ampère equation { u t − log { g − 1 det ( g i j + ∇ i j u ) } = − n log u in M n × ( 0, ∞ ), u ( x, 0 ) = u 0 ( x ) in M n, where M n is a compact complete Riemannian manifold of dimension n ≥ 2, g i j denotes the metric of M n, g = det ( g i j ) > 0 and u 0 ( x ) > 1 is a smooth function. We prove the global existence of solutions.