Search results for "Variable"
showing 10 items of 1674 documents
Exceptional Sets for Quasiconformal Mappings in General Metric Spaces
2008
A theorem of Balogh, Koskela, and Rogovin states that in Ahlfors Q-regular metric spaces which support a p-Poincare inequality, , an exceptional set of -finite (Q−p)- dimensional Hausdorff measure can be taken in the definition of a quasiconformal mapping while retaining Sobolev regularity analogous to that of the Euclidean setting. Through examples, we show that the assumption of a Poincare inequality cannot be removed.
Analytic Properties of Quasiconformal Mappings Between Metric Spaces
2012
We survey recent developments in the theory of quasiconformal mappings between metric spaces. We examine the various weak definitions of quasiconformality, and give conditions under which they are all equal and imply the strong classical properties of quasiconformal mappings in Euclidean spaces. We also discuss function spaces preserved by quasiconformal mappings.
Behandlung eines Goursatproblems mit einer verallgemeinerten Riemannschen Methode
1973
In dieser Arbeit wird ein lineares Goursat problem in zwei Zeit- und einer Raumvariablen behandelt. Die Koeffizienten der betrachteten Differentialgleichung mussen hierbei nach allen Variablen beliebig oft differenzierbar sein und nebst all ihren partiellen Ableitungen bestimmten Wachstumsbeschrankungen genugen. Fur die Inhomogenitat und die Vorgaben werden gesonderte Voraussetzungen gestellt. Zuerst wird fur ein hinsichtlich der Anfangsbedingungen verallgemeinertes Goursatproblem die eindeutige Losbarkeit in der gleichen Funktionenklasse bewiesen, in der die Koeffizienten der Differentialgleichung liegen. Auf Grund dieses Ergebnisses gelingt es dann, mit Hilfe einer verallgemeinerten Riema…
Sobolev Extension on Lp-quasidisks
2021
AbstractIn this paper, we study the Sobolev extension property of Lp-quasidisks which are the generalizations of classical quasidisks. After that, we also find some applications of this property.
THE STATE OF FRACTIONAL HEREDITARY MATERIALS (FHM)
2014
The widespread interest on the hereditary behavior of biological and bioinspired materials motivates deeper studies on their macroscopic ``minimal" state. The resulting integral equations for the detected relaxation and creep power-laws, of exponent $\beta$, are characterized by fractional operators. Here strains in $SBV_{loc}$ are considered to account for time-like jumps. Consistently, starting from stresses in $L_{loc}^{r}$, $r\in [1,\beta^{-1}], \, \, \beta\in(0,1)$ we reconstruct the corresponding strain by extending a result in [42]. The ``minimal" state is explored by showing that different histories delivering the same response are such that the fractional derivative of their differ…
Stabilization of the cohomology of thickenings
2016
For a local complete intersection subvariety $X=V({\mathcal I})$ in ${\mathbb P}^n$ over a field of characteristic zero, we show that, in cohomological degrees smaller than the codimension of the singular locus of $X$, the cohomology of vector bundles on the formal completion of ${\mathbb P}^n$ along $X$ can be effectively computed as the cohomology on any sufficiently high thickening $X_t=V({\mathcal I^t})$; the main ingredient here is a positivity result for the normal bundle of $X$. Furthermore, we show that the Kodaira vanishing theorem holds for all thickenings $X_t$ in the same range of cohomological degrees; this extends the known version of Kodaira vanishing on $X$, and the main new…
Sobolev Spaces and Quasiconformal Mappings on Metric Spaces
2001
Heinonen and I have recently established a theory of quasiconformal mappings on Ahlfors regular Loewner spaces. These spaces are metric spaces that have sufficiently many rectifiable curves in a sense of good estimates on moduli of curve families. The Loewner condition can be conveniently described in terms of Poincare inequalities for pairs of functions and upper gradients. Here an upper gradient plays the role that the length of the gradient of a smooth function has in the Euclidean setting. For example, the Euclidean spaces and Heisenberg groups and the more general Carnot groups admit the type of a Poincare inequality we need. We describe the basics and discuss the associated Sobolev sp…
Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces
2015
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Analytic Bergman operators in the semiclassical limit
2018
Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical Bergman projections on weighted $L^2$ spaces with analytic weights, and show that their kernel functions admit an asymptotic expansion in the class of analytic symbols. As a corollary, we obtain new estimates for asymptotic expansions of the Bergman kernel on $\mathbb{C}^n$ and for high powers of ample holomorphic line bundles over compact complex manifolds.
Removable sets for intrinsic metric and for holomorphic functions
2019
We study the subsets of metric spaces that are negligible for the infimal length of connecting curves; such sets are called metrically removable. In particular, we show that every totally disconnected set with finite Hausdorff measure of codimension 1 is metrically removable, which answers a question raised by Hakobyan and Herron. The metrically removable sets are shown to be related to other classes of "thin" sets that appeared in the literature. They are also related to the removability problems for classes of holomorphic functions with restrictions on the derivative.