Hölder estimates for solutions of parabolic SPDEs

S. B. Kuksin; N. S. Nadirashvili; A. L. Piatnitski

doi:10.1137/S0040585X97979524

Hölder estimates for solutions of parabolic SPDEs

S. B. Kuksin
, N. S. Nadirashvili
, A. L. Piatnitski

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

13 Citations (Scopus)

Abstract

This paper considers second-order stochastic partial differential equations with additive noise given in a bounded domain of Rⁿ. We suppose that the coefficients of the noise are L^p-functions with sufficiently large p. We prove that the solutions are Hölder-continuous functions almost surely (a.s.) and that the respective ?older norms have finite momenta of any order.

Original language	English
Pages (from-to)	157-163
Number of pages	7
Journal	Theory of Probability and its Applications
Volume	47
Issue number	1
DOIs	https://doi.org/10.1137/S0040585X97979524
Publication status	Published - 2003

Keywords

Hölder-continuous function
Stochastic equation

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10.1137/S0040585X97979524

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title = "H{\"o}lder estimates for solutions of parabolic SPDEs",

abstract = "This paper considers second-order stochastic partial differential equations with additive noise given in a bounded domain of Rn. We suppose that the coefficients of the noise are Lp-functions with sufficiently large p. We prove that the solutions are H{\"o}lder-continuous functions almost surely (a.s.) and that the respective ?older norms have finite momenta of any order.",

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author = "Kuksin, \{S. B.\} and Nadirashvili, \{N. S.\} and Piatnitski, \{A. L.\}",

year = "2003",

doi = "10.1137/S0040585X97979524",

language = "English",

volume = "47",

pages = "157--163",

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T1 - Hölder estimates for solutions of parabolic SPDEs

AU - Kuksin, S. B.

AU - Nadirashvili, N. S.

AU - Piatnitski, A. L.

PY - 2003

Y1 - 2003

N2 - This paper considers second-order stochastic partial differential equations with additive noise given in a bounded domain of Rn. We suppose that the coefficients of the noise are Lp-functions with sufficiently large p. We prove that the solutions are Hölder-continuous functions almost surely (a.s.) and that the respective ?older norms have finite momenta of any order.

AB - This paper considers second-order stochastic partial differential equations with additive noise given in a bounded domain of Rn. We suppose that the coefficients of the noise are Lp-functions with sufficiently large p. We prove that the solutions are Hölder-continuous functions almost surely (a.s.) and that the respective ?older norms have finite momenta of any order.

KW - Hölder-continuous function

KW - Stochastic equation

UR - https://www.scopus.com/pages/publications/0037265515

U2 - 10.1137/S0040585X97979524

DO - 10.1137/S0040585X97979524

M3 - Article

SN - 1095-7219

VL - 47

SP - 157

EP - 163

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

IS - 1

ER -

Hölder estimates for solutions of parabolic SPDEs

Abstract

Keywords

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