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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	419-435
Number of pages	17
Journal	Journal des Mathematiques Pures et Appliquees
Volume	99
Issue number	4
DOIs	https://doi.org/10.1016/j.matpur.2012.09.008
Publication status	Published - 1 Apr 2013

Keywords

Calculus of variations
Convexity
Functions with bounded variation
Gaussian measures
Representations formulas
Semicontinuity
Wiener spaces

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10.1016/j.matpur.2012.09.008

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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",

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AU - Goldman, M.

AU - Novaga, M.

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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

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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

Abstract

Keywords

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