In this paper we develop a new approach to nonlinear stochastic partial differential
equations with Gaussian noise. Our aim is to provide an abstract framework which is …

An $\mathrm {L} _1 $-maximal regularity theory for parabolic evolution equations inspired by
the pioneering work of Da Prato and Grisvard is developed. Besides of its own interest, the …

This article focuses on L p-estimates for the square root of elliptic systems of second order in
divergence form on a bounded domain. We treat complex bounded measurable coefficients …

We are concerned with the barotropic compressible Navier–Stokes system in a bounded
domain of R d (with d≥ 2). In a critical regularity setting, we establish local well-posedness …

We consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain
Ω subject to homogeneous Dirichlet boundary conditions. We prove L p-resolvent estimates …

Second-order divergence form operators are studied on an open set with various boundary
conditions. It is shown that the p-ellipticity condition of Carbonaro–Dragičević and Dindoš …

We give a simple argument to obtain L p L^p‐boundedness for heat semigroups associated
to uniformly strongly elliptic systems on R d R^d by using Stein interpolation between …

Abstract Let Ω ⊆ R^ d Ω⊆ R d be open and A a complex uniformly strictly accretive d * dd×
d matrix-valued function on Ω Ω with L^ ∞ L∞ coefficients. Consider the divergence-form …

We consider vector-valued elliptic boundary value problems and parabolic initial-boundary
value problems on abstract Banach spaces of class HT. For a very general class of …

Given a complex, elliptic coefficient function we investigate for which values of p the
corresponding second-order divergence form operator, complemented with Dirichlet …