Representation, relaxation and convexity for variational problems in Wiener spaces

A. Chambolle; M. Goldman; M. Novaga

doi:10.1016/j.matpur.2012.09.008

Representation, relaxation and convexity for variational problems in Wiener spaces

A. Chambolle
, M. Goldman
, M. Novaga

Ecole polytechnique
Dipartimento di Matematica
University of Padova

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

2 Citations (Scopus)

Résumé

We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that extends analogous results valid in the classical Euclidean framework.

langue originale	Anglais
Pages (de - à)	419-435
Nombre de pages	17
journal	Journal des Mathematiques Pures et Appliquees
Volume	99
Numéro de publication	4
Les DOIs	https://doi.org/10.1016/j.matpur.2012.09.008
état	Publié - 1 avr. 2013

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10.1016/j.matpur.2012.09.008

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@article{bfe2742147cc48cbaf54168725ff4196,

title = "Representation, relaxation and convexity for variational problems in Wiener spaces",

abstract = "We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that extends analogous results valid in the classical Euclidean framework.",

keywords = "Calculus of variations, Convexity, Functions with bounded variation, Gaussian measures, Representations formulas, Semicontinuity, Wiener spaces",

author = "A. Chambolle and M. Goldman and M. Novaga",

year = "2013",

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TY - JOUR

T1 - Representation, relaxation and convexity for variational problems in Wiener spaces

AU - Chambolle, A.

AU - Goldman, M.

AU - Novaga, M.

PY - 2013/4/1

Y1 - 2013/4/1

N2 - We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that extends analogous results valid in the classical Euclidean framework.

AB - We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that extends analogous results valid in the classical Euclidean framework.

KW - Calculus of variations

KW - Convexity

KW - Functions with bounded variation

KW - Gaussian measures

KW - Representations formulas

KW - Semicontinuity

KW - Wiener spaces

U2 - 10.1016/j.matpur.2012.09.008

DO - 10.1016/j.matpur.2012.09.008

M3 - Article

AN - SCOPUS:84875672585

SN - 0021-7824

VL - 99

SP - 419

EP - 435

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 4

ER -

Representation, relaxation and convexity for variational problems in Wiener spaces

Résumé

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