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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