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
particular, as KdV possesses only half as many conservation laws as ILW and BO, we observe a novel 2-to-1 collapse of ILW conservation laws to those of KdV, which yields alternating modes of convergence for
