Equivalence and Hölder-Sobolev regularity of solutions for a class of non-autonomous stochastic partial differential equations. (English) Zbl 1026.60080

Sanz-Solé, Marta; Vuillermot, Pierre-A.

Ann. Inst. Henri Poincaré, Probab. Stat. 39, No. 4, 703-742 (2003).

This paper is devoted to a class of non-autonomous semilinear stochastic initial-boundary equations defined in a smooth bounded convex domain and driven by an infinite-dimensional noise which depends on both space and time variables (colored in space, white in time). Four notions of solution are introduced, three of them being equivalent. For these solutions, existence, uniqueness, pointwise boundedness of the moments and the joint space-time Hölder continuity of the solution are obtained under an appropriate integrability condition regarding the covariance operator of the associated Wiener process. This condition may be weakened to obtain existence, uniqueness and regularity of the fourth type of solution.

Reviewer: D.Lepingle (Orléans)

MSC:

60H15

Stochastic partial differential equations (aspects of stochastic analysis)

Keywords:

stochastic partial differential equation; Hölder-Sobolev regularity