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Gradient Estimates on Rd

Published online by Cambridge University Press:  20 November 2018

Feng-Yu Wang
Feng-Yu Wang*
Affiliation:
Department of Mathematics, Beijing Normal University Beijing, 100875 People's Republic of China
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Abstract

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This paper uses both the maximum principle and coupling method to study gradient estimates of positive solutions to Lu = 0 on Rd, where

with (aij) uniformly positive definite and aij,bi € C1(Rd). We obtain some upper bounds of |∇u|/u and ∥∇u∥∞/∥u∥∞, which imply a Harnack inequality and improve the corresponding results proved in Cranston [4]. Besides, two examples show that our estimates can be sharp.

Keywords

58G3258C50gradient estimatecouplingdiffusion process
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 560 - 570
Copyright
Copyright © Canadian Mathematical Society 1994

References

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