Search results for "Funk"
showing 10 items of 623 documents
Pointwise Inequalities for Sobolev Functions on Outward Cuspidal Domains
2019
Abstract We show that the 1st-order Sobolev spaces $W^{1,p}(\Omega _\psi ),$$1<p\leq \infty ,$ on cuspidal symmetric domains $\Omega _\psi $ can be characterized via pointwise inequalities. In particular, they coincide with the Hajłasz–Sobolev spaces $M^{1,p}(\Omega _\psi )$.
Public Network Value for the Next Generation am Beispiel von funk
2018
Die Debatte um die Legitimation des offentlich-rechtlichen Rundfunks hat im digitalen Zeitalter eine neue Dimension erreicht: Insbesondere das junge Publikum wendet sich nicht nur verstarkt den privat-kommerziellen Sendern zu, sondern konsumiert immer haufiger Bewegtbildinhalte im Netz, wo internationale Player wie YouTube oder Netflix an Bedeutung gewinnen. Die Sorge, das junge Publikum komplett zu verlieren, ist deshalb gros. Mit funk – dem „jungen Angebot“ von ARD und ZDF – sollen die 14- bis 29-Jahrigen mithilfe von zielgruppenspezifischen Inhalten nun wieder an die offentlich-rechtliche Marke gebunden werden. Der vorliegende Beitrag nimmt die Markteinfuhrung zum Anlass, die Ausgestaltu…
Neklātienes sacensību organizēšana
2022
Darbā veikta neklātienes sacensību organizēšanas platformas “distantrace.com” funkcionalitātes sistematizācija un izstrādāts šādu sacensību organizēšanas funkcionālais apraksts. Sistematizācijas nolūkos izstrādāts neklātienes sacensību izveidošanas prototips, kā arī prototipa apraksts. Veikts neklātienes sacensību organizēšanas sistēmu funkcionālais salīdzinājums, kā arī pētīts, kādas ir šāda tipa sacensību organizēšanas izmaksas. Analizēti arī dati, kas ietekmē neklātienes sacensību rezultātu korektumu un uz analīzes pamata izstrādāts prototips, kas automātiski pārbauda ierakstīto sporta aktivitāšu datu atbilstību veiktajam sporta aktivitātes veidam.
Zadania sądu egzekucyjnego w postępowaniu cywilnym - właściwość funkcjonalna
2021
Właściwość funkcjonalna w postępowaniu egzekucyjnym wyznacza zakres kompetencji pełnionych przez sąd egzekucyjny, referendarza oraz komornika. Czynności egzekucyjne są wykonywane przez komorników z wyjątkiem czynności zastrzeżonych dla sądów. W ostatnim czasie dochodzi do przekazywania kompetencji sądu egzekucyjnego na rzecz referendarza sądowego. Opracowanie prezentuje zakres uprawnień sądu i referendarza w postępowaniu egzekucyjnym
Density of Lipschitz functions in energy
2020
In this paper, we show that the density in energy of Lipschitz functions in a Sobolev space $N^{1,p}(X)$ holds for all $p\in [1,\infty)$ whenever the space $X$ is complete and separable and the measure is Radon and finite on balls. Emphatically, $p=1$ is allowed. We also give a few corollaries and pose questions for future work. The proof is direct and does not involve the usual flow techniques from prior work. It also yields a new approximation technique, which has not appeared in prior work. Notable with all of this is that we do not use any form of Poincar\'e inequality or doubling assumption. The techniques are flexible and suggest a unification of a variety of existing literature on th…
Singular quasisymmetric mappings in dimensions two and greater
2018
For all $n \geq 2$, we construct a metric space $(X,d)$ and a quasisymmetric mapping $f\colon [0,1]^n \rightarrow X$ with the property that $f^{-1}$ is not absolutely continuous with respect to the Hausdorff $n$-measure on $X$. That is, there exists a Borel set $E \subset [0,1]^n$ with Lebesgue measure $|E|>0$ such that $f(E)$ has Hausdorff $n$-measure zero. The construction may be carried out so that $X$ has finite Hausdorff $n$-measure and $|E|$ is arbitrarily close to 1, or so that $|E| = 1$. This gives a negative answer to a question of Heinonen and Semmes.
Fine properties of functions with bounded variation in Carnot-Carathéodory spaces
2019
Abstract We study properties of functions with bounded variation in Carnot-Caratheodory spaces. We prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of their distributional derivatives. Under an additional assumption on the space, called property R , we show that almost all approximate discontinuities are of jump type and we study a representation formula for the jump part of the derivative.
Universal differentiability sets and maximal directional derivatives in Carnot groups
2019
We show that every Carnot group G of step 2 admits a Hausdorff dimension one `universal differentiability set' N such that every real-valued Lipschitz map on G is Pansu differentiable at some point of N. This relies on the fact that existence of a maximal directional derivative of f at a point x implies Pansu differentiability at the same point x. We show that such an implication holds in Carnot groups of step 2 but fails in the Engel group which has step 3.
Weakly controlled Moran constructions and iterated functions systems in metric spaces
2011
We study the Hausdorff measures of limit sets of weakly controlled Moran constructions in metric spaces. The separation of the construction pieces is closely related to the Hausdorff measure of the corresponding limit set. In particular, we investigate different separation conditions for semiconformal iterated function systems. Our work generalizes well known results on self-similar sets in metric spaces as well as results on controlled Moran constructions in Euclidean spaces.
Characterisation of upper gradients on the weighted Euclidean space and applications
2020
In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and we characterise the minimal weak upper gradient of all Lipschitz functions.