DSpace Collection:
http://hdl.handle.net/10077/3315
Mon, 30 Jan 2023 10:38:19 GMT2023-01-30T10:38:19ZLocal Overdetermined Linear Elliptic Problems in Lipschitz Domains with Solutions Changing Sign
http://hdl.handle.net/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.1-27Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10077/33412009-01-01T00:00:00ZA Nonstandard Proof of the Banach-Steinhaus Theorem
http://hdl.handle.net/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. 185-188Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10077/33402009-01-01T00:00:00ZProblemi di razionalità e unirazionalità: da Ugo Morin ai giorni nostri
http://hdl.handle.net/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. 165-184Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10077/33392009-01-01T00:00:00ZAlmost PSH Functions on Calabi’s Bundles
http://hdl.handle.net/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.139-163Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10077/33382009-01-01T00:00:00Z