\(W^{2,p}\) estimates for the parabolic Monge-Ampère equation
type: Item
instance of: scholarly article
title: \(W^{2,p}\) estimates for the parabolic Monge-Ampère equation
zbMATH Open document ID: 0992.35020
author: Cristian E. Gutiérrez
author: Qingbo Huang
published in: Archive for Rational Mechanics and Analysis
publication date: 2001-11-21T00:00:00Z
review text: This paper is devoted to the parabolic Monge-Ampère operator \[ {\mathcal M}u= -u_t+\det D_x^2u, \] where \(u=u(t,x)\) is convex in \(x\in \mathbb{R}^n\) and nonincreasing in \(t\in R\), and \(D^2u=D_x^2u\) denotes the Hessian of \(u\) with respect to the variable \(x\). The goal of this paper is to show that solutions \(u\) to \({\mathcal M}u=f\) with \(f\) positive, continuous, and \(f_t\) satisfying certain growth conditions, have second derivatives in \(L^p\) for \(0<p< \infty\).
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1676019
zbMATH Keywords: Hessian
zbMATH Keywords: growth conditions
MaRDI profile type: Publication
full work available at URL: s002050100151
OpenAlex ID: W2392329591
DOI: 10.1007/S002050100151
description: scientific article; zbMATH DE number 1676019