Seit dem 1. April 2017 unterstützt für 10 Wochen Julien Lomonaco die AG Festkörpermechanik im Bereich der thermischen Analyse anisotroper Wärmeausbreitung. Organisiert wird der Austausch durch Professor
result is an error estimate for the time-discretisation showing a convergence rate of order (up to) 1/2. It holds with respect to mean square error convergence, whereas previously such a rate for the stochastic
energy norm with respect to convergence in probability, that is convergence of order (almost) 1/2in time and 1 in space. This was previously only known in the space-periodic case, where higher order energy
system behavior. This ties up to the introduction of the appropriate functional setting of critical $L^1$-maximal regularity in Besov spaces. After, giving a descrippion of the system, as well as a motivation […] of the linear Analysis, which is central to have a complete overview on the powerfulness of the $L^1$-maximal regularity-framework. The more likely standard $L^q(L^p)$ setting will also be investigated
steady-states on coarse meshes. In this talk, I share our proposed WB finite volume method for both the 1-D and 2-D SWMHD system. These methods also properly treat the divergence-free condition of the magnetic
the motivation for L^p spaces and present the preliminaries, where we look at the definition for $L^1$ spaces, examples and a proof with graphical representation. We further define equivalence class of
exhibit that such a procedure is possible for $\L^p$-based Sobolev and Besov spaces at the cost of a $1/p$ derivative, and that the optimal range of the trace operator in the said Besov space is actually
for vector-valued functions in L^1 fulfilling a co-canceling differential condition. This work demonstrates that such a property is not just peculiar to the space L^1. Indeed, under the same differential […] well-known to be equivalent to Sobolev inequalities of the same order for domain norms "far" from L^1, but to be weaker otherwise. Recent contributions by Van Schaftingen, by Hernandez, Raita and Spector […] Lorentz-Zygmund spaces. Especially relevant instances of inequalities for domain spaces neighboring L^1 are singled out. This is joined work with Andrea Cianchi and Daniel Spector.
x}(\mathbb{R}_+\times\mathbb{R}^n)$ and then in $L^q_{t}(\mathbb{R}_+, L^p_{x}(\mathbb{R}^n))$, with $1\leqslant p,q\leqslant + \infty$. We will first treat the case $p=2$, introducing fractional Sobolev
coefficient. We prove maximal regularity estimates (including the prominent spaces $W^{1,p}$ and $W^{2,p}$ for $p\in(1,\infty)$ for the velocity field) in bounded domains of minimal regularity. Interestingly
