Semicontinuity in for polyconvex integrals
Viene studiata la semicontinuità rispetto alla topologia di per alcuni funzionali del Calcolo delle Variazioni dipendenti da funzioni a valori vettoriali.
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Emilio Acerbi, Giuseppe Buttazzo, Nicola Fusco (1982)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Viene studiata la semicontinuità rispetto alla topologia di per alcuni funzionali del Calcolo delle Variazioni dipendenti da funzioni a valori vettoriali.
Francescopaolo Montefalcone (2003)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Let be a family of bounded Lipschitz continuous vector fields on . In this paper we prove that if is a set of finite -perimeter then his -perimeter is the limit of the -perimeters of a sequence of euclidean polyhedra approximating in -norm. This extends to Carnot-Carathéodory geometry a classical theorem of E. De Giorgi.
Michel Delfour, Jean-Paul Zolésio (2005)
Control and Cybernetics
Cherif Amrouche, Šárka Nečasová, Jan Sokołowski (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
Material and shape derivatives for solutions to the Dirichlet Laplacian in a half-space are derived by an application of the speed method. The proposed method is general and can be used for shape sensitivity analysis in unbounded domains for the Neumann Laplacian as well as for the elasticity boundary value problems.
G. Anzellotti, E. Ossanna (1995)
Manuscripta mathematica
Frank Morgan (1989)
Inventiones mathematicae
Silvano Delladio (1996)
Annales Polonici Mathematici
We prove generalizations of Meusnier's theorem and Fenchel's inequality for a class of generalized surfaces with curvature measures. Moreover, we apply them to obtain a diameter estimate.
Luis Caffarelli (2003)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Liouville problems in periodic media (i.e. the study of properties of global solutions to PDE) arise both in homogenization and dynamical systems. We discuss some recent results for minimal surfaces and free boundaries.
Francescopaolo Montefalcone (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Let be a -step Carnot group. The first aim of this paper is to show an interplay between volume and -perimeter, using one-dimensional horizontal slicing. What we prove is a kind of Fubini theorem for -regular submanifolds of codimension one. We then give some applications of this result: slicing of functions, integral geometric formulae for volume and -perimeter and, making use of a suitable notion of convexity, called-convexity, we state a Cauchy type formula for -convex sets. Finally,...
Roger Züst (2015)
Analysis and Geometry in Metric Spaces
We give a necessary and sufficient condition for a map deffned on a simply-connected quasi-convex metric space to factor through a tree. In case the target is the Euclidean plane and the map is Hölder continuous with exponent bigger than 1/2, such maps can be characterized by the vanishing of some integrals over winding number functions. This in particular shows that if the target is the Heisenberg group equipped with the Carnot-Carathéodory metric and the Hölder exponent of the map is bigger than...
Silvano Delladio (1997)
Journal für die reine und angewandte Mathematik
Joao Barbosa, Carmo Manfredo do (1984)
Mathematische Zeitschrift
Grégoire Allaire, Frédéric de Gournay, François Jouve, Anca-Maria Toader (2005)
Control and Cybernetics
Dana Nance (1987/1988)
Mathematische Annalen
G. David, S. Semmes (1995/1996)
Séminaire Équations aux dérivées partielles (Polytechnique)
Guy David, Stephen Semmes (1996)
Journées équations aux dérivées partielles
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