Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence

A Agresti, M Veraar - Nonlinearity, 2022 - iopscience.iop.org
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 …

The square root problem for second-order, divergence form operators with mixed boundary conditions on L p

P Auscher, N Badr, R Haller-Dintelmann… - Journal of Evolution …, 2015 - Springer
We show that, under general conditions, the operator (-∇. μ ∇+ 1)^ 1/2 (-∇. μ∇+ 1) 1/2 with
mixed boundary conditions provides a topological isomorphism between W^ 1, p _D (Ω)\rm …

JL Lions' problem on maximal regularity

W Arendt, D Dier, S Fackler - Archiv der Mathematik, 2017 - Springer
JL Lions’ problem on maximal regularity Page 1 Arch. Math. 109 (2017), 59–72 c© 2017
Springer International Publishing 0003-889X/17/010059-14 published online March 27, 2017 …

[HTML][HTML] Lp-estimates for the square root of elliptic systems with mixed boundary conditions

M Egert - Journal of Differential Equations, 2018 - Elsevier
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 …

[HTML][HTML] Existence of weak solutions to a Cahn–Hilliard–Biot system

H Abels, H Garcke, J Haselböck - Nonlinear Analysis: Real World …, 2025 - Elsevier
We prove existence of weak solutions to a diffuse interface model describing the flow of a
fluid through a deformable porous medium consisting of two phases. The system non …

Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets

S Bechtel, M Egert - Journal of Fourier Analysis and Applications, 2019 - Springer
A full interpolation theory for Sobolev functions with smoothness between 0 and 1 and
vanishing trace on a part of the boundary of an open set is established. Geometric …

[PDF][PDF] Hölder estimates for parabolic operators on domains with rough boundary

K Disser, AFM Ter Elst, J Rehberg - ANNALI SCUOLA NORMALE …, 2017 - journals.sns.it
In this paper we investigate linear parabolic, second-order boundaryvalue problems with
mixed boundary conditions on rough domains. Assuming only boundedness/ellipticity on the …

Second order optimality conditions for optimal control of quasilinear parabolic equations

L Bonifacius, I Neitzel - 2017 - bonndoc.ulb.uni-bonn.de
We discuss an optimal control problem governed by a quasilinear parabolic PDE including
mixed boundary conditions and Neumann boundary control, as well as distributed control …

[PDF][PDF] Hardy's inequality for functions vanishing on a part of the boundary

M Egert, R Haller-Dintelmann, J Rehberg - arXiv preprint arXiv:1405.6167, 2014 - arxiv.org
arXiv:1405.6167v2 [math.AP] 16 Feb 2015 Page 1 HARDY’S INEQUALITY FOR FUNCTIONS
VANISHING ON A PART OF THE BOUNDARY MORITZ EGERT, ROBERT …

The Kato square root problem on locally uniform domains

S Bechtel, M Egert, R Haller-Dintelmann - Advances in Mathematics, 2020 - Elsevier
We obtain the Kato square root estimate for second order elliptic operators in divergence
form with mixed boundary conditions on an open and possibly unbounded set in R d under …