1,720,965 research outputs found
Regularity results for solutions to a class of non-autonomous obstacle problems with sub-quadratic growth conditions
No full textBesov regularity for solutions of elliptic equations with variable exponents
No full textWe establish the higher fractional differentiability of the solutions of a problem in divergence form of the type (Formula presented.) The main features consist in assuming that the partial map ξ→A(x,ξ) has p(x)-growth, the datum F is Besov regular and both the partial map x → A(x,ξ) and the function x → p(x) are Orlicz–Besov regular
An example of a functional which is weakly lower semicontinuous on for every but not on
No full textVery degenerate elliptic equations under almost critical Sobolev regularity
No full textWe prove the local Lipschitz continuity and the higher differentiability of local minimizers of functionals of the form F(u,Ω)=∫Ω(F(x,Du(x))+f(x)·u(x))dx with non-autonomous integrand F(x, ζ) which is degenerate convex with respect to the gradient variable. The main novelty here is that the results are obtained assuming that the partial map x → DξF(x,ξ)has weak derivative in the almost critical Zygmund class LnlogαL and the datum f is assumed to belong to the same Zygmund class
Polyconvex functionals and maximum principle
No full textLet us consider continuous minimizers u : , subset of Rn -> Rn of Z F (v) = [|Dv|p + |det Dv|r]dx, , with p > 1 and r > 0; then it is known that every component u alpha of u = (u1, ..., un) enjoys maximum principle: the set of interior points x, for which the value u alpha(x) is greater than the supremum on the boundary, has null measure, that is, Ln({x is an element of , : u alpha(x) > sup partial differential , u alpha}) = 0. If we change the structure of the functional, it might happen that the maximum principle fails, as in the case Z F(v) = [max{(|Dv|p - 1); 0} + |det Dv|r]dx, , with p > 1 and r > 0. Indeed, for a suitable boundary value, the set of the interior points x, for which the value u alpha(x) is greater than the supremum on the boundary, has a positive measure, that is Ln({x is an element of , : u alpha(x) > sup partial differential , u alpha}) > 0. In this paper we show that the measure of the image of these bad points is zero, that is Ln(u({x is an element of , : u alpha(x) > sup partial differential , u alpha})) = 0, provided p > n. This is a particular case of a more general theorem
Higher regularity in congested traffic dynamics
No full textIn this paper, we consider minimizers of integral functionals of the type F(u):=∫Ω[1p(|Du|-1)+p+f·u]dxfor p> 1 in the vectorial case of mappings u: Rn⊃ Ω → RN with N≥ 1. Assuming that f belongs to Ln+σ for some σ> 0 , we prove that H(Du) is continuous in Ω for any continuous function H: RNn→ RNn vanishing on { ξ∈ RNn: | ξ| ≤ 1 }. This extends previous results of Santambrogio and Vespri (Nonlinear Anal 73:3832–3841, 2010) when n= 2 , and Colombo and Figalli (J Math Pures Appl (9) 101(1):94–117, 2014) for n≥ 2 , to the vectorial case N≥ 1
Regularity results for solutions to obstacle problems with Sobolev coefficients
Full text linkWe establish the higher differentiability of solutions to a class of obstacle problems of the type min{∫Ωf(x,Dv(x))dx:v∈Kψ(Ω)}, where ψ is a fixed function called obstacle, Kψ(Ω)={v∈Wloc1,p(Ω,R):v≥ψ a.e. in Ω} and the convex integrand f satisfies p-growth conditions with respect to the gradient variable. We derive that the higher differentiability property of the weak solution v is related to the regularity of the assigned ψ, under a suitable Sobolev assumption on the partial map x↦Dξf(x,ξ). The main novelty is that such assumption is independent of the dimension n and this, in the case p≤n−2, allows us to manage coefficients in a Sobolev class below the critical one W1,n
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
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