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Extremum principles for a general class of saddle functionals

โœ Scribed by Peter Smith

Publisher
Springer Netherlands
Year
1986
Tongue
English
Weight
594 KB
Volume
6
Category
Article
ISSN
0167-8019

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โœฆ Synopsis

The usual notion of a saddle functional in the calculus of variations assumes a , vex/concave structure over the product space of two inner product spaces. Here the idea~ extended to include some convexity in both spaces whilst still retaining an overall saddle property. Dual extremum principles are established for these functionals. Examples include periodic solutions of Duffing's equation, an iterative scheme and a pair of simultaneous partial differential equations which arise in magnetohydrodynamics. (1980). 49H05, 49D10.

AMS (MOS) subject classifications

๐Ÿ“œ SIMILAR VOLUMES

Everywhere regularity for a class of vec
Everywhere regularity for a class of vectorial functionals under subquadratic general growth conditions
โœ F. Leonetti; E. Mascolo; F. Siepe ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 227 KB

We consider the integral functional of the calculus of variations where f : R nN โ†’ R satisfies f (z) = g(|z|) and g is an N-function with subquadratic p-q growth. We prove that minimizers u : โ„ฆ โŠ‚ R n โ†’ R N of such a functional are locally Lipschitz continuous, provided g verifies some additional co