fractional Sobolev spaces $\H^{s}(\mathbb{R}^n)$. Equivalent characterizations with different norms, such as through Littlewood-Paley decompositions or finite differences (Sobolev-Slobodeckij/Gagliardo norms)
Vortrag sollte für alle Mathematik-Interessierten zugänglich sein. Allerdings bietet er erhebliches Suchtpotential, da mehr Fragen offenbleiben als beantwortet werden. Bereits ab 16:30 Uhr gibt es für alle I
The algorithmic advancements are demonstrated for model problems such as the heat equation as well as benchmarks in porous media such as a three-dimensional footing problem. Bereits ab 16:30 Uhr gibt
ed 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 constraint, […] canceling differential operators are offered for general families of rearrangement-invariant spaces, such as the Orlicz spaces and the Lorentz-Zygmund spaces. Especially relevant instances of inequalities
and such a restriction yields a function that lies in an appropriate Besov space with a non-integer amount of regularity. First, we show some basic trace results. We will then exhibit that such a procedure […] a "minimally smooth" boundary. If time permits, we will discuss the optimality and applications of such sharp results.
whose hydrodynamic aspect is modelled by the magneto-hydro-dynamic equations, short MHD equations. Such flows can cover a wide range of Mach and Alfvén numbers. Thus it is very important to have a numerical […] this talk we will discuss the numerical challenges when constructing a efficient numerical scheme for such a multi-scale problem and present a novel structure-preserving scheme. The numerical method is illustrated
receiver coils allows the reconstruction of high-resolution images from undersampled Fourier data such that the acquisition time can be substantially reduced. Mathematically, the parallel MRI reconstruction […] satisfied. Moreover, it has a low computational complexity and fits real MRI data sufficiently well such that it is applicable in practice. The results presented in this talk have been obtained jointly with
demonstrate positive and negative results in this direction. The third deals with topology optimization of such networks. Here, valid inequalities on the binary decision variables are derived using the nonlinear
different case studies. Furthermore, we will briefly review competing distributional regression approaches such as conditional transformation models and distribution regression, density regression, and quantile
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