The nonparametric integral of the calculus of variations as a Weierstrass integral. II: Some applications

DOI10.1016/0022-247X(85)90293-8zbMath0582.49032MaRDI QIDQ1068358

Primo Brandi, Anna Salvadori

Publication date: 1985

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

existenceBurkill integralCesari integralnon-parametric integralsTonelli type theoremweighted generalized area

Mathematics Subject Classification ID

Set-valued set functions and measures; integration of set-valued functions; measurable selections (28B20) Variational problems in a geometric measure-theoretic setting (49Q20) Length, area, volume, other geometric measure theory (28A75)

Related Items (4)

On the nonparametric integral over a bv surface ⋮ On the lower semicontinuity of certain integrals of the calculus of variations ⋮ Nonlinear integration and Weierstrass integral over a manifold, connections with theorems on martingales ⋮ The nonparametric integral of the calculus of variations as a Weierstrass integral: existence and representation

Cites Work

• Sopra i fondamenti di una classe di problemi variazionali dello spazio
• On convergence in area in the generalized sense
• The nonparametric integral of the calculus of variations as a Weierstrass integral: existence and representation
• On the differentiability of functions of several variables
• Sopra l'esistenza dell'estremo assoluto per una classe di problemi di Lagrange in forma parametrica
• L'integrale di Weierstrass non parametrico e quasi additivita
• Quasi additivita e integrali non parametrici 2-dimensionali del calcolo delle variazioni
• Approssimata subadditivita e integrali non parametrici 2-dimensionali del calcolo delle variazioni
• Sopra l'esistenza dell'estremo assoluto per una classe di problemi variazionali di ordine n
• Sopra la semicontinuita degli integrali curvilinei dei problemi variazionali in forma parametrica di ordine n
• Teoremi di semicontinuita inferiore e di approssimazione per le variazioni con peso in \(\mathbb{R}\)
• Burkill-Cesari integrals of quasi additive interval functions
• The theory of the Burkill integral
• Lower-semicontinuity and area functionals. I. The non-parametric case
• Quasi Additive Set Functions and the Concept of Integral Over a Variety
• Extension Problem for Quasi Additive Set Functions and Radon-Nikodym Derivatives
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