http://www.openstarts.units.it:80/dspace/handle/10077/3315 2013-05-25T14:04:40Z http://www.openstarts.units.it:80/dspace/handle/10077/3341 Title: Local Overdetermined Linear Elliptic Problems in Lipschitz Domains with Solutions Changing Sign Authors: Canuto, Bruno; Rial, Diego Abstract: We prove that the only domain $\Omega$ such that there exists a solution to the following overdetermined problem $\Deltau+\omega2u=−1$ in in $\Omega$, u = 0 on $\partial\Omega$, and $\partialnu = c$ on $\partial\Omega$, is the ball B1, independently on the sign of u, if we assume that the boundary $\partial\Omega$ is a perturbation (no necessarily regular) of the unit sphere $\partialB1$ of Rn. Here $\omega2 \neq (\lambdan)n\geq1$ (the eigenvalues of $−\Delta$ in B1 with Dirichlet boundary conditions), and $\omega \Lambda$, where $\Lambda$ is a enumerable set of R+, whose limit points are the values $\lambda1m$, for some integer $m\geq1$, $\lambda1m$ being the mth-zero of the first-order Bessel function I1. Description: pp.1-27 Type: Articolo 2009-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/3340 Title: A Nonstandard Proof of the Banach-Steinhaus Theorem Authors: Vera Sereno, Edith M.; Vera Mendoza, Rigoberto Abstract: The Banach-Steinhaus theorem, also known as Uniform Boundedness Principle, has a standard proof a little bit too long. In this article we will give a real short proof using the nonstandard analysis technique. Description: pp. 185-188 Type: Articolo 2009-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/3339 Title: Problemi di razionalità e unirazionalità: da Ugo Morin ai giorni nostri Authors: Verra, Alessandro Abstract: Unirationality and rationality problems are, in the field of Algebraic Geometry, among the most significant topics of the scientific legacy of Ugo Morin. The paper compares the present state of the art, and its historical evolution, with Morin’s achievements and his brilliant ideas. A special attention to open problems and the newer notion of rational connectivity is payed. Description: pp. 165-184 Type: Articolo 2009-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/3338 Title: Almost PSH Functions on Calabi’s Bundles Authors: Abdesselem, Adnène Ben; Cherrier, Pascal Abstract: We give an explicit lower bound for almost psh functions on some Fano manifolds. These manifolds generalize those introduced by Calabi in [5], and also provide a generalization of the concept of the blowing-up of $\mathbb P_m\mathbb C$ at one point. To this end, we use a method introduced in [4], which consists of studying the behavior of psh functions along some well-chosen holomorphic curves. Description: pp.139-163 Type: Articolo 2009-01-01T00:00:00Z