The \(C^{\alpha}\) regularity of weak solutions of ultraparabolic equations
type: Item
instance of: scholarly article
title: The \(C^{\alpha}\) regularity of weak solutions of ultraparabolic equations
zbMATH Open document ID: 1209.35072
author: Wendong Wang
author: Liqun Zhang
published in: Discrete and Continuous Dynamical Systems
publication date: 2011-03-15T00:00:00Z
review text: The authors consider a class of ultraparabolic equations with measurable coefficients of the form \[ \partial_t \, u= \sum_{i,j=1}^{m_0}X_i(a_{ij}(x,t)X_j\, u )+X_0 u. \] By choosing a new cut-off function, they prove the \(C^{\alpha}\) continuity of weak solutions extending analogous results proved by Lanconelli, Kogoj, Pascucci, Bonfiglioli, Uguzzoni and Polidoro. Their technique is based on a Poincare type inequality and a Harnack type estimate.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35K70
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 5866086
zbMATH Keywords: hypoelliptic
zbMATH Keywords: ultraparabolic
zbMATH Keywords: \(C^{\alpha}\) regularity
MaRDI profile type: Publication
full work available at URL: dcds.2011.29.1261
OpenAlex ID: W2315196406
DOI: 10.3934/DCDS.2011.29.1261
description: scientific article; zbMATH DE number 5866086