Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.40 (2008)

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CONTENTS

Bruno Canuto and Diego Rial
Local Overdetermined Linear Elliptic Problems in Lipschitz Domains with Solutions Changing Sign

Mohammed Ali Toumi
Exponents in R of Elements in a Uniformly Complete Φ-Algebra

Edoardo Ballico
Rank 2 Totally Arithmetically Cohen-Macaulay Vector Bundles on an Abelian Surface with $Num(X) \cong \mathbb Z$

Luca Bortolussi and Andrea Sgarro
A Criterion for the Stochasticity of Matrices with Specified Order Relations

Rachid Benabidallah, Linda Taleb and Hisao Fujita Yashima
Sur le potentiel de pression-gravitation pour le mouvement d’un gaz á transformation adiabatique

Abdelmalek Azizi and Mohammed Taous
Déterminations des corps K = ℚ(√d, √-1) dont les 2-groupes de classes sont de type (2, 4) ou (2, 2, 2)

Mehmet Tekkoyun
Lifts of Structures on Product Manifolds

Adnène Ben Abdesselem and Pascal Cherrier
Almost PSH Functions on Calabi’s Bundles

Alessandro Verra
Problemi di razionalità e unirazionalità da Ugo Morin ai giorni nostri

Edith M. Vera Sereno and Rigoberto Vera Mendoza
A Nonstandard Proof of the Banach-Steinhaus Theorem

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    Local Overdetermined Linear Elliptic Problems in Lipschitz Domains with Solutions Changing Sign
    (EUT - Edizioni Università di Trieste, 2009)
    Canuto, Bruno
    ;
    Rial, Diego
    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.
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