On well-posedness of semilinear stochastic evolution equations on L_p spaces

2015/12/14 by Marinelli, Carlo
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1512.04323

Abstract

We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations on L_p spaces, driven by multiplicative Wiener noise, with a drift term given by an evaluation operator that is assumed to be quasi-monotone and polynomially growing, but not necessarily continuous. In particular, we consider a notion of mild solution ensuring that the evaluation operator applied to the solution is still function-valued, but satisfies only minimal integrability conditions. The proofs rely on stochastic calculus in Banach spaces, monotonicity and convexity techniques, and weak compactness in L₁ spaces.

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