Por Riccardo Scala (University of Rome 1, “La Sapienza”).
Abstract: We introduce the notion of area of the graph of a smooth function and the definition of the corresponding relaxed functional. We discuss some issues related to determine the domain and the exact value of it on singular maps. Finally we show how this question is related to Plateau-type problems with mixed boundary conditions and how to solve it in some specific cases.
Por Wladimir Neves (Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brasil).
Abstract: In this talk, we consider a fractional type degenerate heat equation posed in bounded domains. We show the existence of solutions for measurable and bounded non-negative initial data, and homogeneous Dirichlet boundary condition. The nonlocal diffusion effect relies on an inverse of the s-fractional Laplacian operator, and the solvability is proved for any s , 0 < s < 1.
Por Sebastián Buedo Fernández (University of Santiago de Compostela).
Por Tatsuya Miura (Max Planck Institute for Mathematics in the Sciences, Leipzig).
Por Alberto Bressan (Penn State University).
Por Andrei Zviagin (Voronezh State University, Russia).
Por Jianjun Zhang (Università degli Studi dell'Insubria).
Por Giorgio Saracco (Università degli Studi di Pavia).
Por Alessandro Fonda (Università degli Studi di Udine).
Abstract: We consider periodic perturbations of a central force field having a rotational symmetry, and prove the existence of nearly circular periodic orbits. We thus generalize, in the planar case, some previous bifurcation results obtained by Ambrosetti and Coti Zelati. Our results apply, in particular, to the classical Kepler problem.
Por Rodica Toader (Università degli Studi di Udine).
Abstract: The mathematical formulation of problems in dynamic fracture mechanics leads naturally to the study of the wave equation on domains which vary in time. We provide a notion of solution to the wave equation on a suitable class of time-dependent domains and show existence and uniqueness for the solutions of the Cauchy problem.
The results are obtained in collaboration with G. Dal Maso (SISSA, Trieste).
