Seminario di Analisi Matematica - Non occurrence of the Lavrentiev gap for multidimensional autonomous problems

Relatore: Pierre Bousquet (Université Paul Sabatier Toulouse III)

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Quando

01/03/2022
dalle 14:30 alle 16:00

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Aula B1 (Palazzo Manfredini)

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NON OCCURRENCE OF THE LAVRENTIEV GAP FOR
MULTIDIMENSIONAL AUTONOMOUS PROBLEMS

PIERRE BOUSQUET

 

We establish that the Lavrentiev phenomenon does not occur for autonomous

problems in the multiple integrals Calculus of Variations, provided that the inte-
grand is convex with respect to the gradient variable. The main novelty is that

no other (artificial) restriction is assumed on the integrand or on the domain. The
core of the proof is based on a new approximation result for a parametric version
of the variational problem.

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