Holder norm estimates for elliptic operators on finite and infinite-dimensional spaces

Athreya, Siva R. ; Bass, Richard F. ; Perkins, Edwin A. (2005) Holder norm estimates for elliptic operators on finite and infinite-dimensional spaces Transactions of the American Mathematical Society, 357 . pp. 5001-5029. ISSN 0002-9947

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Official URL: http://www.ams.org/journals/tran/2005-357-12/S0002...

Related URL: http://dx.doi.org/10.1090/S0002-9947-05-03638-X

Abstract

We introduce a new method for proving the estimate Equation Omitted. Where u solves the equation Δu − λu = f. The method can be applied to the Laplacian on R. It also allows us to obtain similar estimates when we replace the Laplacian by an infinite-dimensional Ornstein-Uhlenbeck operator or other elliptic operators. These operators arise naturally in martingale problems arising from measure-valued branching diffusions and from stochastic partial differential equations.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
Keywords:Semigroups; Schauder Estimates; Holder Spaces; Perturbations; Resolvents; Elliptic Operators; Laplacian; Ornstein-Uhlenbeck Processes; Infinite-dimensional Stochastic Differential Equations
ID Code:100384
Deposited On:12 Feb 2018 12:16
Last Modified:12 Feb 2018 12:16

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