On fractional regularity of distributions of functions in Gaussian random variables

We study fractional smoothness of measures on ℝk, that are images of a Gaussian measure under mappings from Gaussian Sobolev classes. As a consequence we obtain Nikolskii–Besov fractional regularity of these distributions under some weak nondegeneracy assumption.

Parabolic p-Laplacian revisited: Global regularity and fractional smoothness

This paper presents an investigation on the existence, fractional and classical regularity in vector-valued Banach spaces for the solutions of a family of evolutive [Formula: see text]-Laplacian-like equations subject to Neumann boundary conditions. Global space-time regularity to the solution and its time derivative in Nikolskii and Slobodeckii spaces is discussed and improved [Formula: see text]-weak regularity for a class of intermediate dual spaces is obtained. Moreover, precise energy estimates showing the influence of the degeneracy pattern of the equation are provided.

Characterization of generalized Orlicz spaces

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz–Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.