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Conical stochastic maximal L^p-regularity for 1leqslant p |
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| Authors: | Pascal Auscher Jan van Neerven Pierre Portal |
| Affiliation: | 1. Laboratoire de Mathématiques, Université Paris-Sud, UMR 8628 du CNRS, 91405?, Orsay, France 2. Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA?, Delft, The Netherlands 3. Laboratoire Paul Painlevé, Université Lille 1, 59655?, Villeneuve d’Ascq, France 4. Mathematical Sciences Institute, Australian National University, John Dedman Building, Acton, ACT, 0200, Australia |
| Abstract: | Let (A = -mathrm{div} ,a(cdot ) nabla ) be a second order divergence form elliptic operator on ({mathbb R}^n) with bounded measurable real-valued coefficients and let (W) be a cylindrical Brownian motion in a Hilbert space (H) . Our main result implies that the stochastic convolution process $$begin{aligned} u(t) = int _0^t e^{-(t-s)A}g(s),dW(s), quad tgeqslant 0, end{aligned}$$ satisfies, for all (1leqslant p |
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