Related papers: On temporal regularity of stochastic convolutions …

In this article we investigate the temporal regularity of strong solutions to the stochastic $p$-\com{L}aplace system in the degenerate setting, $p \in [2,\infty)$, driven by a multiplicative nonlinear stochastic forcing. We establish $1/2$…

We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains…

This paper revisits the H\"{o}lder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces $L^p(\mathcal{O}),$ with $p\geq 2$ and $\mathcal{O}\subset\mathbb{R}^d$ a bounded domain. We find conditions on $p,…

We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains $O \subset R^d$ with both theoretical and numerical purpose. We use N.V. Krylov's framework of…

In the article, integration of temporal functions in (possibly non-UMD) Banach spaces with respect to (possibly non-Gaussian) fractional processes from a finite sum of Wiener chaoses is treated. The family of fractional processes that is…

In the article, Besov-Orlicz regularity of sample paths of stochastic processes that are represented by multiple integrals of order $n\in\mathbb{N}$ is treated. We give sufficient conditions for the considered processes to have paths in the…

In the paper regularity of solutions to stochastic Volterra equations in a separable Hilbert space is studied. Sufficient conditions for the temporal and spatial regularity of stochastic convolutions corresponding to the equations under…

A broad class of possibly non-unique generalized kinetic solutions to hyperbolic-parabolic PDEs is introduced. Optimal regularity estimates in time and space for such solutions to nonlocal, and spatially inhomogeneous variants of the porous…

We derive optimal regularity, in both time and space, for solutions of the Cauchy problem related to a degenerate differential equation in a Banach space X. Our results exhibit a sort of prevalence for space regularity, in the sense that…

In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in…

We provide regularity of solutions to a large class of evolution equations on Banach spaces where the generator is composed of a static principal part plus a non-autonomous perturbation. Regularity is examined with respect to the graph norm…

This paper is devoted to studying stochastic parabolic evolution equations with additive noise in Banach spaces of M-type 2. We construct both strict and mild solutions possessing very strong regularities. First, we consider the linear…

This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations extending our findings in [22] to domains of polyhedral type. In particular, we study the smoothness in the specific scale…

We report on a time regularity result for stochastic evolutionary PDEs with monotone coefficients. If the diffusion coefficient is bounded in time without additional space regularity we obtain a fractional Sobolev type time regularity of…

Regularity estimates in time and space for solutions to the porous medium equation are shown in the scale of Sobolev spaces. In addition, higher spatial regularity for powers of the solutions is obtained. Scaling arguments indicate that…

We prove optimal regularity estimates in Sobolev spaces in time and space for solutions to stochastic porous medium equations. The noise term considered here is multiplicative, white in time and coloured in space. The coefficients are…

Optimal second-order regularity in the space variables is established for solutions to Cauchy-Dirichlet problems for nonlinear parabolic equations and systems of $p$-Laplacian type, with square-integrable right-hand sides and initial data…

We study the symmetric stochastic $p$-Stokes system, $p \in (1,\infty)$, in a bounded domain. The results are two-folded. First, we show that in the context of analytically weak solutions the stochastic pressure -- related to non-divergence…

We study the sample path regularity of the solutions of a class of spde's which are second order in time and that includes the stochastic wave equation. Non-integer powers of the spatial Laplacian are allowed. The driving noise is white in…

This paper develops the necessary ingredients for the variational approach of initial boundary-value problems of parabolic partial differential equations on a fixed spatial domain containing evolving subdomains. In particular, we introduce…