On the maximum principle for linear parabolic equations

Hung Ju Kuo; Neil S. Trudinger

doi:10.1007/s10898-007-9249-7

On the maximum principle for linear parabolic equations

Hung Ju Kuo, Neil S. Trudinger^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

We prove extensions of our previous estimates for linear elliptic equations with inhomogeneous terms in L ^p spaces, p n to linear parabolic equations with inhomogeneous terms in L ^p , p n + 1. As with the elliptic case, our results depend on restrictions on parabolicity determined by certain subcones of the positive cone . They also extend the maximum principle of Krylov for the case p = n + 1, corresponding to the usual parabolicity.

Original language	English
Pages (from-to)	495-500
Number of pages	6
Journal	Journal of Global Optimization
Volume	40
Issue number	1-3
DOIs	https://doi.org/10.1007/s10898-007-9249-7
Publication status	Published - Mar 2008

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title = "On the maximum principle for linear parabolic equations",

abstract = "We prove extensions of our previous estimates for linear elliptic equations with inhomogeneous terms in L p spaces, p n to linear parabolic equations with inhomogeneous terms in L p , p n + 1. As with the elliptic case, our results depend on restrictions on parabolicity determined by certain subcones of the positive cone . They also extend the maximum principle of Krylov for the case p = n + 1, corresponding to the usual parabolicity.",

keywords = "Hessian integrals, Linear parabolic equations, Maximum principles, Parabolic Hessian equation",

author = "Kuo, \{Hung Ju\} and Trudinger, \{Neil S.\}",

year = "2008",

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T1 - On the maximum principle for linear parabolic equations

AU - Kuo, Hung Ju

AU - Trudinger, Neil S.

PY - 2008/3

Y1 - 2008/3

N2 - We prove extensions of our previous estimates for linear elliptic equations with inhomogeneous terms in L p spaces, p n to linear parabolic equations with inhomogeneous terms in L p , p n + 1. As with the elliptic case, our results depend on restrictions on parabolicity determined by certain subcones of the positive cone . They also extend the maximum principle of Krylov for the case p = n + 1, corresponding to the usual parabolicity.

AB - We prove extensions of our previous estimates for linear elliptic equations with inhomogeneous terms in L p spaces, p n to linear parabolic equations with inhomogeneous terms in L p , p n + 1. As with the elliptic case, our results depend on restrictions on parabolicity determined by certain subcones of the positive cone . They also extend the maximum principle of Krylov for the case p = n + 1, corresponding to the usual parabolicity.

KW - Hessian integrals

KW - Linear parabolic equations

KW - Maximum principles

KW - Parabolic Hessian equation

UR - https://www.scopus.com/pages/publications/38849189463

U2 - 10.1007/s10898-007-9249-7

DO - 10.1007/s10898-007-9249-7

M3 - Article

SN - 0925-5001

VL - 40

SP - 495

EP - 500

JO - Journal of Global Optimization

JF - Journal of Global Optimization

IS - 1-3

ER -

On the maximum principle for linear parabolic equations

Abstract

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