We discover a new minimality property of the absolute minimizers of supremal functionals, whose variational problems are also known as L∞ variational problems. In particular for every minimizer v of the quasi-convex functional (Formula Presented) we consider the set (Formula Presented) suitably defined. If u is an absolute minimizer, we give a structure result for A(u) and we show that (Formula Presented) for every minimizer v.
A PROPERTY OF ABSOLUTE MINIMIZERS IN L∞ CALCULUS OF VARIATIONS AND OF SOLUTIONS OF THE ARONSSON-EULER EQUATION / Brizzi C.; De Pascale L.. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - STAMPA. - 28:(2023), pp. 287-310. [10.57262/ade028-0304-287]
A PROPERTY OF ABSOLUTE MINIMIZERS IN L∞ CALCULUS OF VARIATIONS AND OF SOLUTIONS OF THE ARONSSON-EULER EQUATION
Brizzi C.;De Pascale L.
2023
Abstract
We discover a new minimality property of the absolute minimizers of supremal functionals, whose variational problems are also known as L∞ variational problems. In particular for every minimizer v of the quasi-convex functional (Formula Presented) we consider the set (Formula Presented) suitably defined. If u is an absolute minimizer, we give a structure result for A(u) and we show that (Formula Presented) for every minimizer v.
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