1,721,190 research outputs found
Convergence faible et capacités
No full textThe author generalizes the classical notions of weak convergence and strong convergence in measure theory. This is done by taking a set E together with two partial orders such that the first order satisfies the countable Dedekind condition (that is, every nonempty countable subset of E which is bounded above has a supremum), and the second order is also subject to certain conditions. Now take the set of all positive-valued functions on E which are increasing with respect to the first order. The usual concepts of measure theory, such as upper and lower envelopes of a function, weak convergence, etc., are adapted to this general setting. The results so developed are then applied to capacities and to certain special classes of capacities
Calculus of Variations and Applications: international conference to celebrate Gianni Dal Maso's 65th Birthday, 2020: 27 January - 2 February, Trieste (Italy)
No full textAn International Conference held in SISSA to celebrate Gianni Dal Maso's 65th Birthday and an exceptional opportunity to present the state of the art of modern methods in the Calculus of Variations and their applications and to stimulate exchange of ideas and knowledge, through a rich selection of talks by leading experts in the field. (2020-01-27
Quasistatic Limit of a Dynamic Viscoelastic Model with Memory
No full textWe study the behaviour of the solutions to a dynamic evolution problem for a viscoelastic model with long memory, when the rate of change of the data tends to zero. We prove that a suitably rescaled version of the solutions converges to the solution of the corresponding stationary problem
An introduction to Γ-convergence
No full textThe last twentyfive years have seen an increasing interest for variational convergences and for their applications to different fields, like homogenization theory, phase transitions, singular perturbations, boundary value problems in wildly perturbed domains, approximation of variatonal problems, and non- smooth analysis. Among variational convergences, De Giorgi's r-convergence plays a cen- tral role for its compactness properties and for the large number of results concerning r -limits of integral functionals. Moreover, almost all other varia- tional convergences can be easily expressed in the language of r -convergence. This text originates from the notes of the courses on r -convergence held by the author in Trieste at the International School for Advanced Studies (S. I. S. S. A. ) during the academic years 1983-84,1986-87, 1990-91, and in Rome at the Istituto Nazionale di Alta Matematica (I. N. D. A. M. ) during the spring of 1987. This text is far from being a treatise on r -convergence and its appli- cations
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