Displaying similar documents to “Homogenization of periodic nonconvex integral functionals in terms of Young measures”

Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach

Filippo Cagnetti, Rodica Toader (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

A new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [G. Dal Maso and C. Zanini, 137 (2007) 253–279] is recovered. In this case, the convergence of the discrete time approximations is improved.

Large deviations, central limit theorems and L convergence for Young measures and stochastic homogenizations

Julien Michel, Didier Piau (2010)

ESAIM: Probability and Statistics

Similarity:

We study the stochastic homogenization processes considered by Baldi (1988) and by Facchinetti and Russo (1983). We precise the speed of convergence towards the homogenized state by proving the following results: (i) a large deviations principle holds for the Young measures; if the Young measures are evaluated on a given function, then (ii) the speed of convergence is bounded in every L norm by an explicit rate and (iii) central limit theorems hold. In dimension 1, we apply these...

On the lower semicontinuity of supremal functionals defined on measures

Michele Gori (2006)

Bollettino dell'Unione Matematica Italiana

Similarity:

In this paper we consider two particular classes of supremal functionals defined on Radon measures and we find necessary and sufficient conditions for their lower semicontinuity with respect to the weak* convergence. Some applications to the minimization of functionals defined on BV are presented.

Can interestingness measures be usefully visualized?

Robert Susmaga, Izabela Szczech (2015)

International Journal of Applied Mathematics and Computer Science

Similarity:

The paper presents visualization techniques for interestingness measures. The process of measure visualization provides useful insights into different domain areas of the visualized measures and thus effectively assists their comprehension and selection for different knowledge discovery tasks. Assuming a common domain form of the visualized measures, a set of contingency tables, which consists of all possible tables having the same total number of observations, is constructed. These...

Korovkin-type theorems for almost periodic measures

Silvia-Otilia Corduneanu (2002)

Colloquium Mathematicae

Similarity:

Some Korovkin-type theorems for spaces containing almost periodic measures are presented. We prove that some sets of almost periodic measures are test sets for some particular nets of positive linear operators on spaces containing almost periodic measures. We consider spaces which contain almost periodic measures defined by densities and measures which can be represented as the convolution between an arbitrary measure with finite support (or an arbitrary bounded measure) and a fixed...

Research Article. Multiscale Analysis of 1-rectifiable Measures II: Characterizations

Matthew Badger, Raanan Schul (2017)

Analysis and Geometry in Metric Spaces

Similarity:

A measure is 1-rectifiable if there is a countable union of finite length curves whose complement has zero measure. We characterize 1-rectifiable Radon measures μ in n-dimensional Euclidean space for all n ≥ 2 in terms of positivity of the lower density and finiteness of a geometric square function, which loosely speaking, records in an L2 gauge the extent to which μ admits approximate tangent lines, or has rapidly growing density ratios, along its support. In contrast with the classical...