LIPSCHITZ CONTINUITY FOR ENERGY INTEGRALS WITH VARIABLE EXPONENTS

A regularity result for integrals of the Calculus of Variations with variable exponents is presented. Precisely, we prove that any vector-valued minimizer of an energy integral over an open set WHRn, with variable exponent p(x) in the Sobolev class W1; r loc W for some r > n, is locally Lipschitz continuous in W and an a priori estimate holds

Existence of evolutionary variational solutions via the calculus of variations

Abstract In this paper we introduce a purely variational approach to time dependent problems, yielding the existence of global parabolic minimizers, that is ∫ 0 T ∫ Ω [ u ⋅ ∂ t φ + f ( x , D u ) ] d x d t ⩽ ∫ 0 T ∫ Ω f ( x , D u + D φ ) d x d t , whenever T > 0 and φ ∈ C 0 ∞ ( Ω × ( 0 , T ) , R N ) . For the integrand f : Ω × R N n → [ 0 , ∞ ] we merely assume convexity with respect to the gradient variable and coercivity. These evolutionary variational solutions are obtained as limits of maps depending on space and time minimizing certain convex variational functionals. In the simplest situation, with some growth conditions on f, the method provides the existence of global weak solutions to Cauchy–Dirichlet problems of parabolic systems of the type ∂ t u − div D ξ f ( x , D u ) = 0 in Ω × ( 0 , ∞ )

Quasiconvex quadratic forms in two dimensions

Abstract. Let f and g be two quadratic forms in R'. Iff(~) is positive where g(~) = 0, ~ ~ 0, then we show that there exists a real A such that f -Ag is positive definite. As a consequence we obtain a new description of the old characterization by Terpstra [19] of quasiconvex quadratic forms in two dimensions

Інституціональні можливості трудового потенціалу в контексті державного управління інституційними змінами

Обґрунтовано можливість використання механізму трудового потенціалу як складової інституціональних змін системи трудових можливостей для інституційного розвитку. Викладено теоретико-методологічні узагальнення щодо місця інституту держави в межах інституціональних перетворень, а також її ролі у формуванні інституціонального середовища для розвитку трудових можливостей суспільства.In this article there's grounded the possibility of using the mechanism of labor potential, as part of institutional change of employment opportunities for development. In addition, the article provides theoretical and methodological generalizations about a place within the institution of state of institutional changes and its role in shaping the institutional environment for the development of labour opportunities of society. The result of the findings of the paper is to state administration of labor potential

Parabolic equations and the bounded slope condition

Abstract In this paper we establish the existence of Lipschitz-continuous solutions to the Cauchy Dirichlet problem of evolutionary partial differential equations { ∂ t u − div D f ( D u ) = 0 in Ω T , u = u o on ∂ P Ω T . The only assumptions needed are the convexity of the generating function f : R n → R , and the classical bounded slope condition on the initial and the lateral boundary datum u o ∈ W 1 , ∞ ( Ω ) . We emphasize that no growth conditions are assumed on f and that – an example which does not enter in the elliptic case – u o could be any Lipschitz initial and boundary datum, vanishing at the boundary ∂Ω, and the boundary may contain flat parts, for instance Ω could be a rectangle in R n

Robot-era project: Preliminary results on the system usability

The European project Robot-Era is an ambitious integrated project (FP7-ICT-2011.5.4), which objective is the development of advanced robotic services, integrated in intelligent environments, to provide independent living to older people. In order to guarantee the matching of the users� need and the demands, two loops of experimentation were conceived, in realistic and real setting. The aim of the paper is to described the methods applied and the main results coming from the first experimental loop, concerning the degree of usability of the interfaces and provide guidelines for testing socially assistive robots with older people. � Springer International Publishing Switzerland 2015

INFN ScienzaPerTutti: 20 years of science for society

A groundbreaking and ambitious project took shape within the Istituto Nazionale di Fisica Nuclare (INFN) community 20 years ago. The driving aim was the intent to popularize physics, and all this started through a web portal. Since then, the general public and, in particular, students and teachers have been engaged with cutting edge topics of modern research in particle and nuclear physics, astroparticle, theoretical and applied physics. During the 20 years from its birth, the ScienzaPerTutti project evolved in many different directions, becoming a reference point in the Italian landscape, with an average of 3000 contacts every day on the web pages and thousands of followers on the facebook profile. The project encompasses a variety of multimedia products like didactic units, research materials, infographics, interviews, book reviews, and, more recently, podcasts. A particular feature of many of these activities is a constant call to action to directly involve the audience, providing a continuous challenge for the ScienzaPerTutti editorial board to improve contents and devise new approaches. This contribution focuses on some of these activities, even if it does not provide an exhaustive description of all the programmes and opportunities that are offered to our public for lack of space. Finally, we provide an outlook on new activities