Imperial College London
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ProfessorDanCrisan

Faculty of Natural Sciences, Department of Mathematics

Professor of Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8489d.crisan Website

 
 
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Location

 

670Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Crisan:2016:10.1098/rspa.2016.0442,
author = {Crisan, DO and Ottobre, M},
doi = {10.1098/rspa.2016.0442},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
title = {Pointwise gradient bounds for degenerate semigroups (of UFG type)},
url = {http://dx.doi.org/10.1098/rspa.2016.0442},
volume = {472},
year = {2016}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - In this paper we consider diffusion semigroups generated by second order differentialoperators of degenerate type. The operators that we consider do not, in general, satisfy theH¨ormander condition and are not hypoelliptic. In particular, instead of working under the H¨ormanderparadigm, we consider the so-called UFG condition, introduced by Kusuoka and Strook in theeighties. The UFG condition is weaker than the uniform H¨ormander condition, the smoothing effecttaking place only in certain directions (rather than in every direction, as it is the case when theH¨ormander condition is assumed). Under the UFG condition, Kusuoka and Strook deduced sharpsmall time asymptotic bounds for the derivatives of the semigroup in the directions where smoothingoccurs. In this paper, we study the large time asymptotics for the gradients of the diffusionsemigroup in the same set of directions and under the same UFG condition. In particular, we identifyconditions under which the derivatives of the diffusion semigroup in the smoothing directionsdecay exponentially in time. This paper constitutes therefore a stepping stone in the analysis ofthe long time behaviour of diffusions which do not satisfy the H¨ormander condition
AU  - Crisan,DO
AU  - Ottobre,M
DO  - 10.1098/rspa.2016.0442
PY  - 2016///
SN  - 1364-5021
TI  - Pointwise gradient bounds for degenerate semigroups (of UFG type)
T2  - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
UR  - http://dx.doi.org/10.1098/rspa.2016.0442
UR  - http://hdl.handle.net/10044/1/41748
VL  - 472
ER  -
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