Search results for "Equality."
showing 10 items of 1308 documents
Maximal function estimates and self-improvement results for Poincaré inequalities
2018
Our main result is an estimate for a sharp maximal function, which implies a Keith–Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces. peerReviewed
On the continuity of discrete maximal operators in Sobolev spaces
2014
We investigate the continuity of discrete maximal operators in Sobolev space W 1;p (R n ). A counterexample is given as well as it is shown that the continuity follows under certain sucient assumptions. Especially, our research verifies that for the continuity in Sobolev spaces the role of the partition of the unity used in the construction of the maximal operator is very delicate.
Extensions and Imbeddings
1998
AbstractWe establish a connection between the Sobolev imbedding theorem and the extendability of Sobolev functions. As applications we give geometric criteria for extendability and give a result on the dependence of the extension property on the exponentp.
Orlicz–Sobolev extensions and measure density condition
2010
Abstract We study the extension properties of Orlicz–Sobolev functions both in Euclidean spaces and in metric measure spaces equipped with a doubling measure. We show that a set E ⊂ R satisfying a measure density condition admits a bounded linear extension operator from the trace space W 1 , Ψ ( R n ) | E to W 1 , Ψ ( R n ) . Then we show that a domain, in which the Sobolev embedding theorem or a Poincare-type inequality holds, satisfies the measure density condition. It follows that the existence of a bounded, possibly non-linear extension operator or even the surjectivity of the trace operator implies the measure density condition and hence the existence of a bounded linear extension oper…
Weighted norm inequalities in a bounded domain by the sparse domination method
2019
AbstractWe prove a local two-weight Poincaré inequality for cubes using the sparse domination method that has been influential in harmonic analysis. The proof involves a localized version of the Fefferman–Stein inequality for the sharp maximal function. By establishing a local-to-global result in a bounded domain satisfying a Boman chain condition, we show a two-weight p-Poincaré inequality in such domains. As an application we show that certain nonnegative supersolutions of the p-Laplace equation and distance weights are p-admissible in a bounded domain, in the sense that they support versions of the p-Poincaré inequality.
Approximation of Elliptic Hemivariational Inequalities
1999
From the previous chapter we know that there exist many important problems in mechanics in which constitutive laws are expressed by means of nonmonotone, possibly multivalued relations (nonmonotone multivalued stress-strain or reaction-displacement relations,e.g). The resulting mathematical model leads to an inclusion type problem involving multivalued nonmonotone mappings or to a substationary type problem for a nonsmooth, nonconvex superpotential expressed in terms of calculus of variation. It is the aim of this chapter to give a detailed study of a discretization of such a type of problems including the convergence analysis. Here we follow closely Miettinen and Haslinger, 1995, Miettinen…
Robust stabilisation of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities
2013
This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality–based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired…
L'uguale e il diverso. Come le diseguaglianza deprimono il capitale sociale
2017
Come si creano e come si distruggono lo spirito di cooperazione, la solidarietà, la lealtà, la reciprocità, la fiducia? Quali sono le condizioni che favoriscono (o deprimono) la formazione di capitale sociale? La risposta a questa domanda può illuminare numerosi fenomeni contemporanei quali la crescita della propensione alla chiusura e all’esclusione e il ritorno di manifestazioni discriminatorie, xenofobe e razziste. Anche le peggiori performance economiche del Mezzogiorno possono essere illuminate dalla risposta alla domanda su come si crea (e si distrugge) il capitale sociale.
Regional Income Inequality in Spain 1860–2015
2018
How has regional economic inequality evolved since 1860? Is there a relationship between initial per-capita income and regional growth rates? Is there any relation between the evolution of regional inequality and the economic development process in Spain? In order to answer these questions, a number of different indicators of inequality are offered in this chapter. Then the patterns of convergence or divergence followed by Spanish regions from the mid-nineteenth century to the present are studied. Regional income inequality rose in the early stages of economic development and then declined. However, with high levels of development, around the 1980s, a change of trend is observed. In other w…
Plural Paths for Interweaving Diversity in Palermo
2008
The most recent ethnic movements and cultural contacts are modifying the city nature all over the world, and in these years even the most fringe European areas are witnessing an increase in cultural and social mixité. Currently we can assert that the city is not an unitary system any more, instead is composed of multiple (often non-homogeneous) groups which express new forms and demands of space use. In this context of fast changes, the various ethnic groups coming to European cities are not the only stakeholders of diversity. There are also cultural groups which have remained separate until now, each one rooted in a restricted part of the city, according to models that are obsolete nowaday…