On a non-standard convex regularization and the relaxation of unbounded integral functionals of the calculus of variations.
Sull'omogeneizzazione di un problema variazionale con vincoli sul gradiente
We prove a compactness and representation theorem for the -convergence of sequences of convex integral functionals of Variational Calculus with constraints on the gradient. We describe the limit problem for the Homogenization concerning functionals of such a type.
Un teorema di compattezza per la -convergenza di funzionali non coercitivi
We prove a compactness and representation theorem for the -convergence of sequences of convex integral functionals of Variational Calculus, which are not coercive and satisfy non-uniform boundedness assumptions.
Filtrazione di un fluido in un mezzo non omogeneo tridimensionale
We prove the existence of a unique solution for a free boundary problem relative to the stationary flow between two water reservoirs of different levels separated by a non-homogeneous dam with variable cross section.
Homogenization of a monotone problem in a domain with oscillating boundary
On integral representation, relaxation and homogenization for unbounded functionals
A theory of integral representation, relaxation and homogenization for some types of variational functionals taking extended real values and possibly being not finite also on large classes of regular functions is presented. Some applications to gradient constrained relaxation and homogenization problems are given.
Alle origini del Giornale di Matematiche di Battaglini
In questo lavoro studiamo le origini del Giornale di Matematiche, il secondo giornale italiano in ordine di anzianità completamente dedicato alla matematica, fondato a Napoli nel 1863. Vengono messe soprattutto in evidenza i legami con alcune esperienze risalenti a prima dell’unificazione nazionale e la messa a fuoco della linea editoriale.
On the unique extension problem for functionals of the calculus of variations
By drawing inspiration from the treatment of the non parametric area problem, an abstract functional is considered, defined for every open set in a given class of open subsets of and every function in , and verifying suitable assumptions of measure theoretic type, of invariance, convexity, and lower semicontinuity. The problem is discussed of the possibility of extending it, and of the uniqueness of such extension, to a functional verifying analogous properties, but defined in wider families...
Homogenization of a monotone problem in a domain with oscillating boundary
We study the asymptotic behaviour
of the following nonlinear problem:
in a domain Ω
Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set
The paper is a continuation of a previous work of the same authors dealing with homogenization processes for some energies of integral type arising in the modeling of rubber-like elastomers. The previous paper took into account the general case of the homogenization of energies in presence of pointwise oscillating constraints on the admissible deformations. In the present paper homogenization processes are treated in the particular case of fixed constraints set, in which minimal coerciveness hypotheses...
Homogenization of Neumann problems for unbounded integral functionals
Si studia l'omogeneizzazione di problemi di tipo Neumann per funzionali integrali del Calcolo delle Variazioni definiti su funzioni soggette a vincoli puntuali di tipo oscillante sul gradiente, in ipotesi minimali sui vincoli. I risultati ottenuti sono dedotti mediante l'introduzione di nuove tecniche di -convergenza, unitamente ad un risultato di ricostruzione per funzioni affini a tratti, che permettono la dimostrazione di un teorema generale di omogeneizzazione per funzionali integrali a valori...
Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set
The paper is a continuation of a previous work of the same authors dealing with homogenization processes for some energies of integral type arising in the modeling of rubber-like elastomers. The previous paper took into account the general case of the homogenization of energies in presence of pointwise oscillating constraints on the admissible deformations. In the present paper homogenization processes are treated in the particular case of fixed constraints set, in which minimal coerciveness hypotheses...
Il Fondo Stampacchia
In questa nota, descriviamo i documenti acquisiti dal Dipartimento di Matematica e Applicazioni “Renato Caccioppoli” dell’Università “Federico II” di Napoli appartenuti al matematico Guido Stampacchia. Il fondo, donato dagli eredi del matematico, consiste prevalentemente di lavori e versioni preliminari di lavori, relazioni a congressi, lettere con più di 300 corrispondenti, documenti riguardanti le sue attività all’interno di organismi quali l’U.M.I., il C.I.M.E., l’I.A.C. e la sua carriera.
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