Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence
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 …
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 …
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 …
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 …
divergence form on a bounded domain. We treat complex bounded measurable coefficients …
[HTML][HTML] Existence of weak solutions to a Cahn–Hilliard–Biot system
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 …
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
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 …
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 …
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 …
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 …
VANISHING ON A PART OF THE BOUNDARY MORITZ EGERT, ROBERT …
The Kato square root problem on locally uniform domains
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 …
form with mixed boundary conditions on an open and possibly unbounded set in R d under …