[HTML][HTML] 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 …
A universal variational framework for parabolic equations and systems
We propose a variational approach to solve Cauchy problems for parabolic equations and
systems independently of regularity theory for solutions. This produces a universal and …
systems independently of regularity theory for solutions. This produces a universal and …
H\" older Regularity for Domains of Fractional Powers of Elliptic Operators with Mixed Boundary Conditions
R Haller, H Meinlschmidt, J Rehberg - arXiv preprint arXiv:2210.03451, 2022 - arxiv.org
This work is about global H\" older regularity for solutions to elliptic partial differential
equations subject to mixed boundary conditions on irregular domains. There are two main …
equations subject to mixed boundary conditions on irregular domains. There are two main …
Nonautonomous maximal parabolic regularity for nonsmooth quasilinear parabolic systems
H Meinlschmidt - arXiv preprint arXiv:2312.13852, 2023 - arxiv.org
In this paper we are concerned with $ L^ p $-maximal parabolic regularity for abstract
nonautonomous parabolic systems and their quasilinear counterpart in negative Sobolev …
nonautonomous parabolic systems and their quasilinear counterpart in negative Sobolev …
Dimension estimate for the two-sided points of planar Sobolev extension domains
J Takanen - Proceedings of the American Mathematical Society, 2023 - ams.org
In this paper we give an estimate for the Hausdorff dimension of the set of two-sided points
of the boundary of bounded simply connected Sobolev $ W^{1, p} $-extension domain for …
of the boundary of bounded simply connected Sobolev $ W^{1, p} $-extension domain for …