Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.32 (2000)

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https://www.openstarts.units.it/handle/10077/4161

CONTENTS

M. Guidorzi
A remark on partial regularity of minimizers of quasiconvex integrals of higher order

M.K.R.S.Veera Kumar
Between semi-closed sets and semi-pre-closed set

Klaudiusz Wójcik
Remark on subharmonic solutions of periodic planar systems

R. Herrera
Verlinde-type formulae and twistor transform

Darko Zubrinic
Positive solutions of quasilinear elliptic systems with the natural growth in the gradient

Youssèf Ben Cheikh
Decomposition of some hypergeometric polynomials with respect to the cyclic group of order n

Maurizio Badii
Existence and uniqueness of periodic solutions for a quasilinear parabolic problem

Pierpaolo Esposito
Uniqueness and multiplicity for perturbations of the Yamabe problem on Sⁿ

Maciej Smolka
Relaxed parabolic problems

Camillo Costantini, Alessandro Fedeli and Attilio Le Donne
Filters and pathwise connectification

Fabrizio Colombo
Continuous dependence results for an inverse problem in the theory of combustion of materials with memory

Ph. Clément and O. W.van Gaans
An analytical introduction to stochastic differential equations: Part I - the Langevin equation

Details

Editorial policy The journal Rendiconti dell’Istituto di Matematica dell’università di Trieste publishes original articles in all areas of mathematics. Special regard is given to research papers, but attractive expository papers may also be considered for publication. The journal usually appears in one issue per year. Additional issues may however be published. In particular, the Managing Editors may consider the publication of supplementary volumes related to some special events, like conferences, workshops, and advanced schools. All submitted papers will be refereed. Manuscripts are accepted for review with the understanding that the work has not been published before and is not under consideration for publication elsewhere. Our journal can be obtained by exchange agreements with other similar journals.

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Now showing 1 - 12 of 12

Uniqueness and multiplicity for perturbations of the Yamabe problem on $S^n$
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Esposito, Pierpaolo
Motivated by an uniqueness result for linear perturbations with constant coefficients of the conformal laplacian on the sphere, we investigate, via a finite dimensional reduction, more general perturbations of the conformal laplacian, exibiting cases in which uniqueness fails
1089 423
An analytical introduction to stochastic differential equations: Part I - the Langevin equation
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Clément, Ph.
;
van Gaans, O. W.
We present an introduction to the theory of stochastic differential equations, motivating and explaining ideas from the point of view of analysis. First the notion of white noise is developed, introducing at the same time probabilistic tools. Then the one dimensional Langevin equation is formulated as a deterministic integral equation with a parameter. Its solution leads to stochastic convolution, which is defined as a Riemann-Stieltjes integral. It is shown that the parameter dependence yields a Gaussian system, of which the means and covariances arde computed. We conclude by introducing briefly the notion of invariant measure and the associated Kolmogorov equations.
1091 669
A Remark on Partial Regularity of Minimizers of Quasiconvex Integrals of Higher Order
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Guidorzi, M.
We prove partial regularity of minimizers of strictly quasiconvex functionals of the form $I\left(u\right)=\int_{\Omega}F\left(D^{k}u\right)dx,$ where the intergrand grows as $\mid\xi\mid^{p}$.
771 463
Between semi-closed sets and semi-pre-closed set
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Veera Kumar, M.K.R.S.
In this paper a new class of sets, namely $\psi-\mathbf{closed\: set}$ is introduced for topological spaces. This class falls strictly in between the class of semi-closed sets and the class of semipreclosed sets. This class also sits strictly in between the class of semi-closed sets and the class of semi-generalized closed sets. We also introduce and study a new class of spaces, namely $\mathbf{semi-}\textrm{T}_{1/3}\:\mathbf{spaces}$. Further we introduce and study $\psi-\mathbf{continuous}$ maps and $\psi-\mathbf{irresolute}$ maps.
1355 723
Filters and pathwise connectification
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Costantini, Camillo
;
Fedeli, Alessandro
;
Le Donne, Attilio
Let p be a free open-filter on a Hausdorff space X. In this paper we investigate when $X \cup {p}$ can be densely embedded in a pathwise connected $T_2$-space. The main part of the paper is devoted to the cases where X is the rational or the real line.
1408 427
Verlinde-type formulae and twistor transform
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Herrera, Rafael
We study certain aspects of the topology of six moduli spaces of orthogonal vector bundles over Riemann surfaces, with genus between 2 and 7, in order to find generalizations of the well-known Verlinde formula and the Newstead conjectures.
1050 513
Positive solutions of quasilinear elliptic systems with the natural growth in the gradient
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Zubrinic, Darko
We study the problem of existence and nonexistence of positive, spherically symmetric solutions of a quasilinear elliptic system involving p-Laplacians, with the natural growth in the gradient on the right-hand sfide. The existence proof is constructive, with solutions possessing explicit integral representation. We also obtain various qualitative results. The elliptic system is studied by relating it to the corresponding system of singular ODE's of the first order.
985 515
Decomposition of some hypergeometric polynomials with respect to the cyclic group of order $n$
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Ben Cheikh, Youssèf
Let $\left\{ P_{m}\right\} _{m\geq0}$ be a sequence of polynomials with complex coefficients and let n be an arbitrary positive integer. The components with respect to the cyclic group of order n of the polynomial $P_{m},m=0,1,...,$ are given by: \[ \left(P_{m}\right)_{\left[n,k\right]}\left(z\right)=\frac{1}{n}\overset{n-1}{\overset{\sum}{l=0}}\;\omega_{n}^{-kl}P_{m}\left(\omega_{n}^{l}z\right)\:,\quad k=0,1,...,n-1\;, \] where $\omega_{n}=exp\left(\frac{2i\pi}{n}\right)$. In this paper, we consider two class of hypergeometric polynomials, the Brafman polynomials and the Srivastava-Panda polynomials. For the components of these polynomials, we establish hypergeometric representations, differential equations and generating functions.
754 364
Remark on subharmonic solutions of periodic planar systems
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Wójcik, Klaudiusz
Let W be a periodic isolating segment for the periodic planar system. Assume that time O section W$_{0}$ is a topological manifold with boundary and $H\left(W_{0},W_{0}^{-}\right)\neq0$ where W$^{-}$ is the exit set of W. Then there is a subharmonic solution.
984 369
Relaxed parabolic problems
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Smolka, Maciej
Let $G_{n}$ be a sequence of open subsets of a given open and bounded $\Omega\subset\mathbb{R}^{N}$. We study the asymptotic behaviour of the solutions of parabolic equations $u_{n}'+Au_{n}=f_{n}\:\textrm{on}\: G_{n}$. Assuming that the right-hand sides $f_{n}$ and the initial conditions converge in a proper way we find the form of the limit problem without any additional hypothesis on $G_{n}$. Our method is based on the notion of elliptic $\gamma^{A}$-convergence.
927 374
Continuous dependence results for an inverse problem in the theory of combustion of materials with memory
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Colombo, Fabrizio
We prove theorems of continuous dependence on the data for both direct and inverse problems for semilinear integrodifferential equations. Such results are applied to the specific case of the combustion of a material with memory.
982 395
Existence and uniqueness of periodic solutions for a quasilinear parabolic problem
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Badii, Maurizio
We are concerned with the existence and uniqueness of the nonnegative periodic weak solution to a quasilinear parabolic problem of degenerate type, which describes a mathematical model in petroleum engineering. The existence of periodic solutions is established by means of the Schauder fixed point Theorem applied to the Poincaré map. Instead, the uniqueness of the periodic solution is proved under the assumption that $b(\varphi^-1)$ is Hölder continuous of order 1/2, adapting a technique utilized in the study of nonlinear hyperbolic equations.
970 385

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