Second derivative estimates for uniformly elliptic operators on Riemannian manifolds
type: Item
instance of: scholarly article
title: Second derivative estimates for uniformly elliptic operators on Riemannian manifolds
zbMATH Open document ID: 1315.58015
author: Soojung Kim
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2014-11-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1404.5036
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 6366907
zbMATH Keywords: fully nonlinear elliptic equation
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: \(W^{2,\varepsilon}\)-estimates
zbMATH Keywords: ABP method
MaRDI profile type: Publication
OpenAlex ID: W2962966707
arXiv ID: 1404.5036
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Wikidata QID: Q115342983
DOI: 10.1016/J.NA.2014.09.024
review text: The author obtains a uniform \(W^{2,\varepsilon}\)-estimate for solutions of the fully nonlinear uniformly elliptic equation NEWLINE\[NEWLINE F(D^2u,x)=f(x)\quad \text{in}\;B_R(z_0)\subset M, NEWLINE\]NEWLINE where \(M\) is a Riemannian manifold with lower bound for the sectional curvature. The approach relies on the Aleksandrov-Bakelman-Pucci method.
description: scientific article; zbMATH DE number 6366907