Second-order subelliptic operators on Lie groups. III: Hölder continuous coefficients
type: Item
instance of: scholarly article
title: Second-order subelliptic operators on Lie groups. III: Hölder continuous coefficients
zbMATH Open document ID: 0953.22010
author: A. F. M. ter Elst
author: Derek W. Robinson
published in: Calculus of Variations and Partial Differential Equations
publication date: 2001-01-22T00:00:00Z
full work available at URL: secondorder-subelliptic-operators-on-lie-groups-iii-hoelder-continuous-coefficients(b15fe457-8edf-498e-a587-57df52e4f8ed).html
review text: [Parts I and II by the same authors in Acta Appl. Math. 59, 299-331 (1999; see the preceding review) and Prog. Nonlin. Differential Equations Appl. 42, 103-142 (Basel 2000), respectively.] The paper is devoted to the study of relations between the smoothness properties of the coefficients of second-order subelliptic operators \(H\) on a connected Lie group \(G\) with smoothness of the associated semigroup kernel. The principal coefficients of the operator \(H\) are assumed to be Hölder continuous for \(H\) written in divergence form and at least once differentiable otherwise. It is established that the semigroup kernel is almost one degree more differentiable than the coefficients, and the kernel and its derivatives satisfy Gaussian bounds. If the operator \(H\) is in nondivergence form the improvement in smoothness is almost two degrees, and the Gaussian bounds are still valid.
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 1333048
zbMATH Keywords: fuzzy metric space
zbMATH Keywords: Fredholm and Volterra integral equations
zbMATH Keywords: solution
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: second-order subelliptic operators
Wikidata QID: Q115387769
reviewed by: Yuri I. Karlovich
MaRDI profile type: Publication
OpenAlex ID: W2015752333
DOI: 10.1007/S005260050129
description: scientific article; zbMATH DE number 1333048