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Nikolaj Nikolaevich Bogolyubov e il Calcolo delle Variazioni

Giulia FantiElvira Mascolo — 2012

La Matematica nella Società e nella Cultura. Rivista dell'Unione Matematica Italiana

In questa nota presentiamo a parte iniziale della vastissima opera del fisico matematico N.N. Bogolyubov relativa allo studio dei problemi non convessi del Calcolo delle Variazioni. Il suo contributo innanzitutto ha un valore storico: infatti è il primo autore che studia, con tecniche completamente originali, problemi a cui non sipossono applicare i Metodi diretti del Calcolo della Variazioni. In ragione poi del loro intrinseco valore scientifico, ci è sembrato interessante presentare, anche con...

Problemi quasi ellittici in spazi di Sobolev con peso

Daniela GiachettiElvira Mascolo — 1977

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Boundary value problems for linear quasi-elliptic A + σ -type operators with variable coefficients are studied in the unbounded region of 𝐑 n , definited by x k > 0 , k = 1 , , n ; σ means a perturbation whose behaviour is assigned at infinity and in the angular points of the domain. It is proved that the operator related to the problem has closed range and finite dimensional null space. The study is developed within a new class of dissimetric Sobolev weighted spaces.

Everywhere regularity for vectorial functionals with general growth

Elvira MascoloAnna Paola Migliorini — 2003

ESAIM: Control, Optimisation and Calculus of Variations

We prove Lipschitz continuity for local minimizers of integral functionals of the Calculus of Variations in the vectorial case, where the energy density depends explicitly on the space variables and has general growth with respect to the gradient. One of the models is F u = Ω a ( x ) [ h | D u | ] p ( x ) d x with h a convex function with general growth (also exponential behaviour is allowed).

Everywhere regularity for vectorial functionals with general growth

Elvira MascoloAnna Paola Migliorini — 2010

ESAIM: Control, Optimisation and Calculus of Variations

We prove Lipschitz continuity for local minimizers of integral functionals of the Calculus of Variations in the vectorial case, where the energy density depends explicitly on the space variables and has general growth with respect to the gradient. One of the models is F u = Ω a ( x ) [ h | D u | ] p ( x ) d x with a convex function with general growth (also exponential behaviour is allowed).

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