Brownian trajectory is a regular lateral boundary for the heat equation

N. V. Krylov

doi:10.1137/S0036141002402980

Brownian trajectory is a regular lateral boundary for the heat equation

N. V. Krylov

School of Mathematics

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

12 Scopus citations

Abstract

The one-dimensional heat equation in the domain x > w_t, t > 0, is considered. Here w_t is a trajectory of Brownian motion. For almost any trajectory, it is proved that if the boundary data are continuous, then the solution is continuous in the closure of the domain. The proof is based on Davis's law of square root for Brownian motion or on its weaker version, which is obtained by using the theory of stochastic partial differential equations.

Original language	English (US)
Pages (from-to)	1167-1182
Number of pages	16
Journal	SIAM Journal on Mathematical Analysis
Volume	34
Issue number	5
DOIs	https://doi.org/10.1137/S0036141002402980
State	Published - 2003

Keywords

Fine properties of Brownian motion
Heat equation in irregular cylinders
Stochastic partial differential equations

Publisher link

10.1137/S0036141002402980

Find It

Find It at U of M Libraries

Cite this

@article{27ae1653d3e1417f85a09c6e42089db9,

title = "Brownian trajectory is a regular lateral boundary for the heat equation",

abstract = "The one-dimensional heat equation in the domain x > wt, t > 0, is considered. Here wt is a trajectory of Brownian motion. For almost any trajectory, it is proved that if the boundary data are continuous, then the solution is continuous in the closure of the domain. The proof is based on Davis's law of square root for Brownian motion or on its weaker version, which is obtained by using the theory of stochastic partial differential equations.",

keywords = "Fine properties of Brownian motion, Heat equation in irregular cylinders, Stochastic partial differential equations",

author = "Krylov, \{N. V.\}",

year = "2003",

doi = "10.1137/S0036141002402980",

language = "English (US)",

volume = "34",

pages = "1167--1182",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "5",

}

TY - JOUR

T1 - Brownian trajectory is a regular lateral boundary for the heat equation

AU - Krylov, N. V.

PY - 2003

Y1 - 2003

N2 - The one-dimensional heat equation in the domain x > wt, t > 0, is considered. Here wt is a trajectory of Brownian motion. For almost any trajectory, it is proved that if the boundary data are continuous, then the solution is continuous in the closure of the domain. The proof is based on Davis's law of square root for Brownian motion or on its weaker version, which is obtained by using the theory of stochastic partial differential equations.

AB - The one-dimensional heat equation in the domain x > wt, t > 0, is considered. Here wt is a trajectory of Brownian motion. For almost any trajectory, it is proved that if the boundary data are continuous, then the solution is continuous in the closure of the domain. The proof is based on Davis's law of square root for Brownian motion or on its weaker version, which is obtained by using the theory of stochastic partial differential equations.

KW - Fine properties of Brownian motion

KW - Heat equation in irregular cylinders

KW - Stochastic partial differential equations

UR - https://www.scopus.com/pages/publications/0242596346

UR - https://www.scopus.com/pages/publications/0242596346#tab=citedBy

U2 - 10.1137/S0036141002402980

DO - 10.1137/S0036141002402980

M3 - Article

AN - SCOPUS:0242596346

SN - 0036-1410

VL - 34

SP - 1167

EP - 1182

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 5

ER -

Brownian trajectory is a regular lateral boundary for the heat equation

Abstract

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this