Regularisation by multiplicative noise for reaction-diffusion equations.

We consider the stochastic reaction-diffusion equation in 1 + 1 dimensions driven by multiplicative space-time white noise, with a distributional drift belonging to a Besov-Hölder space with any regularity index strictly larger than - 1 . We assume that the diffusion coefficient is a regular function which is bounded away from zero. By using a combination of stochastic sewing techniques and Malliavin calculus, we show that the equation admits a unique solution.