Potentials on abstract Wiener space

René Carmona

doi:10.1016/0022-1236(77)90025-8

Potentials on abstract Wiener space

René Carmona

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Abstract

The infinite dimensional Green measure g is shown to be a product measure and this provides sufficient conditions for the existence and the differentiability of potentials. Moreover, it is shown how such conditions can be used to prove that if f is Lip and if we set u = Gf, then first D²u is Lip too and second u satisfies Δu = -2f for a wide class of functions f with arbitrary support.

Original language	English (US)
Pages (from-to)	215-231
Number of pages	17
Journal	Journal of Functional Analysis
Volume	26
Issue number	3
DOIs	https://doi.org/10.1016/0022-1236(77)90025-8
State	Published - Nov 1977
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis

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10.1016/0022-1236(77)90025-8

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title = "Potentials on abstract Wiener space",

abstract = "The infinite dimensional Green measure g is shown to be a product measure and this provides sufficient conditions for the existence and the differentiability of potentials. Moreover, it is shown how such conditions can be used to prove that if f is Lip and if we set u = Gf, then first D2u is Lip too and second u satisfies Δu = -2f for a wide class of functions f with arbitrary support.",

author = "Ren{\'e} Carmona",

year = "1977",

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N2 - The infinite dimensional Green measure g is shown to be a product measure and this provides sufficient conditions for the existence and the differentiability of potentials. Moreover, it is shown how such conditions can be used to prove that if f is Lip and if we set u = Gf, then first D2u is Lip too and second u satisfies Δu = -2f for a wide class of functions f with arbitrary support.

AB - The infinite dimensional Green measure g is shown to be a product measure and this provides sufficient conditions for the existence and the differentiability of potentials. Moreover, it is shown how such conditions can be used to prove that if f is Lip and if we set u = Gf, then first D2u is Lip too and second u satisfies Δu = -2f for a wide class of functions f with arbitrary support.

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U2 - 10.1016/0022-1236(77)90025-8

DO - 10.1016/0022-1236(77)90025-8

M3 - Article

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VL - 26

SP - 215

EP - 231

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 3

ER -

Potentials on abstract Wiener space

Abstract

All Science Journal Classification (ASJC) codes

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