Séminaire Analyse
organisé par l'équipe Analyse
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Thomas Jaffard
Hölder regularity of distributional volume forms
7 mai 2026 - 11:00Salle de conférences IRMA
Let f, g1, . . . , gd : Rd −→ R be continuous functions. When the functions g1, . . . , gd are of class C1, identifying the d-form f dg1 ∧ · · · ∧ dgd with the continuous function f det(dg) allows one to define the integral ∫_Ω f dg1 ∧ · · · ∧ dgd = ∫_Ω f(x) det(dg(x)) dx, for a bounded Borel set Ω ⊂ Rd. If the functions g1, . . . , gd are not differentiable, it is not clear how to give a meaning to the object f dg1 ∧ · · · ∧ dgd, nor even how to define certain integrals of the form ∫ f dg1 ∧ · · · ∧ dgd. Under regularity assumptions of the type introduced by Züst, we adopt a distributional viewpoint to give a meaning to the object f dg1 ∧ · · · ∧ dgd itself. This approach allows one to define the corresponding integrals, by duality, over more general domains, including sets with fractal boundaries, and to extend integrability results previously obtained by Züst, Alberti–Stepanov–Trevisan, and Bouafia. This talk is based on the preprint available at https://arxiv.org/abs/2510.20427. -
Anatole Gaudin
TBA
11 juin 2026 - 11:00Salle de conférences IRMA