Characterization of Besov spaces with dominating mixed smoothness by differences

Published · Annales de l’Institut Henri Poincaré / B : Probabilites et statistiques, 55 (2019) 3, pp. 1765-1796. We prove a priori estimates in $L_\infty$ for a class of quasilinear stochastic partial differential equations. The estimates are obtained independently of the ellipticity constant $arepsilon$ and thus imply analogous estimates for…

Published · Journal de mathématiques pures et appliquées, 128 (2019), pp. 225-263. The present article is devoted to well-posedness by noise for the continuity equation. Namely, we consider the continuity equation with non-linear and partially degenerate stochastic perturbations in divergence form. We prove the…

Published · Archive for rational mechanics and analysis, 233 (2019) 1, pp. 249-322. We prove the pathwise well-posedness of stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise. As a consequence, the generation of a random dynamical system is obtained. This extends…