Harnack Inequalities for Stochastic Partial Differential Equations by Feng-Yu Wang

Author:Feng-Yu Wang
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

where W(t) is a cylindrical Brownian motion on with respect to a complete filtered probability space . See [10, 36, 72, 73] for equations with a time-dependent linear operator and a multivalued nonlinear term.

Definition 3.1.1

An -valued progressively measurable process is called a mild solution to (3.1) if for every t ∈ [0,T],

(3.2)

and almost surely

To ensure the existence and uniqueness of the solution, we shall assume the following: (A3.1) For every s > 0 and t ∈ [0, T], with

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