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Variational integrals for elliptic complexes

Flavia GiannettiAnna Verde — 2000

Studia Mathematica

We discuss variational integrals which are defined on differential forms associated with a given first order elliptic complex. This general framework provides us with better understanding of the concepts of convexity, even in the classical setting D ' ( n , ) D ' ( n , n ) c u r l D ' ( n , n × n )

On the continuity of degenerate -harmonic functions

Flavia GiannettiAntonia Passarelli di Napoli — 2012

ESAIM: Control, Optimisation and Calculus of Variations

We study the regularity of finite energy solutions to degenerate -harmonic equations. The function (), which measures the degeneracy, is assumed to be subexponentially integrable, it verifies the condition exp(()) ∈ . The function () is increasing on  [0,∞[  and satisfies the divergence condition 1 P ( t ) t 2 d t = .

On weak Hessian determinants

Luigi D'OnofrioFlavia GiannettiLuigi Greco — 2005

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

We consider and study several weak formulations of the Hessian determinant, arising by formal integration by parts. Our main concern are their continuity properties. We also compare them with the Hessian measure.

Divergence forms of the infinity-Laplacian.

Luigi D'OnofrioFlavia GiannettiTadeusz IwaniecJuan ManfrediTeresa Radice — 2006

Publicacions Matemàtiques

The central theme running through our investigation is the infinity-Laplacian operator in the plane. Upon multiplication by a suitable function we express it in divergence form, this allows us to speak of weak infinity-harmonic function in W1,2. To every infinity-harmonic function u we associate its conjugate function v. We focus our attention to the first order Beltrami type equation for h= u + iv

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