1,721,046 research outputs found
On the integral representation of variational functionals on BD
Full text linkFollowing the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with bounded deformation. Mild additional continuity assumptions are required on the functionals
Approximation of SBV functions with possibly infinite jump set
No full textWe prove an approximation result for functions u∈SBV(Ω;Rm) such that ∇u is p-integrable, 1≤p<∞, and g0(|[u]|) is integrable over the jump set (whose Hn−1 measure is possibly infinite), for some continuous, nondecreasing, subadditive function g0, with g0−1(0)={0}. The approximating functions uj are piecewise affine with piecewise affine jump set; the convergence is that of L1 for uj and the convergence in energy for |∇uj|p and g([uj],νujavax.xml.bind.JAXBElement@4d3684be) for suitable functions g. In particular, uj converges to u BV-strictly, area-strictly, and strongly in BV after composition with a bilipschitz map. If in addition Hn−1(Ju)<∞, we also have convergence of Hn−1(Jujavax.xml.bind.JAXBElement@7ed7bf7f) to Hn−1(Ju)
Phase-Field Approximation of a Vectorial, Geometrically Nonlinear Cohesive Fracture Energy
No full textWe consider a family of vectorial models for cohesive fracture, which may incorporate SO(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}-invariance. The deformation belongs to the space of generalized functions of bounded variation and the energy contains an (elastic) volume energy, an opening-dependent jump energy concentrated on the fractured surface, and a Cantor part representing diffuse damage. We show that this type of functional can be naturally obtained as Gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}-limit of an appropriate phase-field model. The energy densities entering the limiting functional can be expressed, in a partially implicit way, in terms of those appearing in the phase-field approximation
Monotonicity formulas for obstacle problems with Lipschitz coefficients
Full text linkWe prove quasi-monotonicity formulas for classical obstacle-type problems with energies being the sum of a quadratic form with Lipschitz coefficients, and a Hölder continuous linear term. With the help of those formulas we are able to carry out the full analysis of the regularity of free-boundary points following the approaches by Caffarelli, Weiss and Monneau
Multi-value microstructural descriptors for complex materials: analysis of ground states
Full text linkA multi-scale and multi-field description of material microstructures which distinguish at every point multiple microstructural individuals is analyzed paying attention to the determination of equilibrium configurations. Rigid bodies with microstructure represented by means of Q−valued maps from the reference place to the manifold of microstructural shapes are considered first. In that case, just microenergetics is considered and macroscopic motion neglected. Then, the stage is enlarged up to include deformable bodies suffering large strains, endowed with energies of Ginzburg-Landau type with respect to the microstructural descriptor fields. In both cases, conditions for semicontinuity of the relevant energies and the existence of ground states are provided
Improved estimate of the singular set of Dir-minimizing Q-valued functions via an abstract regularity result
Full text linkIn this note we prove an abstract version of a recent quantitative stratifcation priciple introduced by Cheeger and Naber (Invent. Math., 191 (2013), no. 2, 321-339; Comm. Pure Appl. Math., 66 (2013), no. 6, 965-990). Using this general regularity result paired with an ε-regularity theorem we provide a new estimate of the Minkowski dimension of the set of higher multiplicity points of a Dir-minimizing Q-valued function. The abstract priciple is applicable to several other problems: we recover recent results in the literature and we obtain also some improvements in more classical contexts
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Lower semicontinuous functionals for Almgren's multiple valued functions
Full text linkWe consider general integral functionals on the Sobolev spaces of multiple valued functions introduced by Almgren. We characterize the semicontinuous ones and recover earlier results of Mattila in [10] as a particular case. Moreover, we answer positively to one of the questions raised by Mattila in the same paper
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