Fonctions BV dans triplet de Gelfand et le problème de réflexion sur un ensemble convexe d'un espace de Hilbert

Michael Röckner; Rongchan Zhu; Xiangchan Zhu

doi:10.1016/j.crma.2010.10.018

Fonctions BV dans triplet de Gelfand et le problème de réflexion sur un ensemble convexe d'un espace de Hilbert

Translated title of the contribution: BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space

Michael Röckner^*
, Rongchan Zhu
, Xiangchan Zhu

^*Corresponding author for this work

Bielefeld University
CAS - Institute of Applied Mathematics
Peking University

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

1 Citation (Scopus)

Abstract

In this Note we introduce BV functions in a Gelfand triple, which is an extension of BV functions in Ambrosio et al., preprint [1], by using Dirichlet form theory. By this definition, we can consider the stochastic reflection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set Γ We prove the existence and uniqueness of a strong solution of this problem when Γis a regular convex set. The result is also extended to the non-symmetric case. Finally, we extend our results to the case when Γ=K_α, where K_α={f∈L²(0,1)|f≥-α},α ≥0.

Translated title of the contribution	BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space
Original language	French
Pages (from-to)	1175-1178
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	348
Issue number	21-22
DOIs	https://doi.org/10.1016/j.crma.2010.10.018
Publication status	Published - Nov 2010
Externally published	Yes

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title = "Fonctions BV dans triplet de Gelfand et le probl{\`e}me de r{\'e}flexion sur un ensemble convexe d'un espace de Hilbert",

abstract = "In this Note we introduce BV functions in a Gelfand triple, which is an extension of BV functions in Ambrosio et al., preprint [1], by using Dirichlet form theory. By this definition, we can consider the stochastic reflection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set Γ We prove the existence and uniqueness of a strong solution of this problem when Γis a regular convex set. The result is also extended to the non-symmetric case. Finally, we extend our results to the case when Γ=Kα, where Kα=\{f∈L2(0,1)|f≥-α\},α ≥0.",

author = "Michael R{\"o}ckner and Rongchan Zhu and Xiangchan Zhu",

year = "2010",

month = nov,

doi = "10.1016/j.crma.2010.10.018",

language = "法语",

volume = "348",

pages = "1175--1178",

journal = "Comptes Rendus Mathematique",

issn = "1631-073X",

publisher = "Academie des sciences",

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T1 - Fonctions BV dans triplet de Gelfand et le problème de réflexion sur un ensemble convexe d'un espace de Hilbert

AU - Röckner, Michael

AU - Zhu, Rongchan

AU - Zhu, Xiangchan

PY - 2010/11

Y1 - 2010/11

N2 - In this Note we introduce BV functions in a Gelfand triple, which is an extension of BV functions in Ambrosio et al., preprint [1], by using Dirichlet form theory. By this definition, we can consider the stochastic reflection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set Γ We prove the existence and uniqueness of a strong solution of this problem when Γis a regular convex set. The result is also extended to the non-symmetric case. Finally, we extend our results to the case when Γ=Kα, where Kα={f∈L2(0,1)|f≥-α},α ≥0.

AB - In this Note we introduce BV functions in a Gelfand triple, which is an extension of BV functions in Ambrosio et al., preprint [1], by using Dirichlet form theory. By this definition, we can consider the stochastic reflection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set Γ We prove the existence and uniqueness of a strong solution of this problem when Γis a regular convex set. The result is also extended to the non-symmetric case. Finally, we extend our results to the case when Γ=Kα, where Kα={f∈L2(0,1)|f≥-α},α ≥0.

UR - https://www.scopus.com/pages/publications/78349313041

U2 - 10.1016/j.crma.2010.10.018

DO - 10.1016/j.crma.2010.10.018

M3 - 文章

AN - SCOPUS:78349313041

SN - 1631-073X

VL - 348

SP - 1175

EP - 1178

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 21-22

ER -

Fonctions BV dans triplet de Gelfand et le problème de réflexion sur un ensemble convexe d'un espace de Hilbert

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