Gradient estimate on convex domains and applications

Feng Yu Wang; Lixin Yan

doi:10.1090/S0002-9939-2012-11480-7

Gradient estimate on convex domains and applications

Feng Yu Wang^*, Lixin Yan

^*Corresponding author for this work

Research output: Contribution to journal › Article

13 Citations (Scopus)

Abstract

By solving the Skorokhod equation for reflecting diffusion processes on a convex domain, gradient estimates for the associated Neumann semigroup are derived. As applications, functional/Harnack inequalities are established for the Neumann semigroup. When the domain is bounded, the gradient estimates are applied to the study of Riesz transforms and regularity of the inhomogeneous Neumann problems on convex domains.

Original language	English
Pages (from-to)	1067-1081
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	141
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-2012-11480-7
Publication status	Published - 2013

Keywords

Gradient estimates for Neumann semigroup
Green operator
Hardy space
Neumann problem
Reflecting diffusion process

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10.1090/S0002-9939-2012-11480-7

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title = "Gradient estimate on convex domains and applications",

abstract = "By solving the Skorokhod equation for reflecting diffusion processes on a convex domain, gradient estimates for the associated Neumann semigroup are derived. As applications, functional/Harnack inequalities are established for the Neumann semigroup. When the domain is bounded, the gradient estimates are applied to the study of Riesz transforms and regularity of the inhomogeneous Neumann problems on convex domains.",

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AB - By solving the Skorokhod equation for reflecting diffusion processes on a convex domain, gradient estimates for the associated Neumann semigroup are derived. As applications, functional/Harnack inequalities are established for the Neumann semigroup. When the domain is bounded, the gradient estimates are applied to the study of Riesz transforms and regularity of the inhomogeneous Neumann problems on convex domains.

KW - Gradient estimates for Neumann semigroup

KW - Green operator

KW - Hardy space

KW - Neumann problem

KW - Reflecting diffusion process

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