We prove an L q theory result for generalized Stokes system on a C 2,1 domain complemented with the perfect slip boundary conditions and under Φ−growth conditions. Since the interior regularity was obtained in [3], a regularity up to the boundary is an aim of this paper. In order to get the main result, we use Calderón–Zygmund theory and the method developed in [1]. We obtain higher integrabili...

it is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. we introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. we deal with vietoris and hausdorff continuity concepts.stability of microperiodi...

The contribution of assembled phonology in reading English was examined in the lexical decision task by comparing two markers: regularity effects and phonological priming. Strategic control was assessed by manipulating the phonological lexicality of the foils: Experiment 1 used legal nonwords, whereas Experiment 2 used pseudohomophones. Replicating existing findings, null regularity effects wer...

In this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints. Our analysis is based on various concepts of second order tangent sets and parametric duality. We introduce a condition, called second order regularity, under which there is no gap between the corresponding second order necessary and second order sufficient conditions. We show t...

We consider the large-scale regularity of solutions to second-order linear elliptic equations with random coefficient fields. In contrast to previous works on regularity theory for random elliptic operators, our interest is in the regularity at the boundary: We consider problems posed on the halfspace with homogeneous Dirichlet boundary conditions and derive an associated C1,α-type large-scale ...

We investigate sectoriality and maximal regularity in L-LSobolev spaces for the structurally damped plate equation with DirichletNeumann (clamped) boundary conditions. We obtain unique solutions with optimal regularity for the inhomogeneous problem in the whole space, in the half-space, and in bounded domains of class C. It turns out that the first-order system related to the scalar equation on...

On December 3, 2012, following the Third Abel conference, in honor of Endre Szemerédi, Terence Tao posted on his blog a proof of the spectral version of Szemerédi’s regularity lemma. This, in turn, proves the original version.