Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable

Ben Andrews; Julie Clutterbuck

doi:10.1016/j.jde.2009.01.024

Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable

Ben Andrews^*, Julie Clutterbuck

^*Corresponding author for this work

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

14 Citations (Scopus)

Abstract

We bound the modulus of continuity of solutions to quasilinear parabolic equations in one space variable in terms of the initial modulus of continuity and elapsed time. In particular we characterize those equations for which the Lipschitz constants of solutions can be bounded in terms of their initial oscillation and elapsed time.

Original language	English
Pages (from-to)	4268-4283
Number of pages	16
Journal	Journal of Differential Equations
Volume	246
Issue number	11
DOIs	https://doi.org/10.1016/j.jde.2009.01.024
Publication status	Published - 1 Jun 2009

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10.1016/j.jde.2009.01.024

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title = "Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable",

abstract = "We bound the modulus of continuity of solutions to quasilinear parabolic equations in one space variable in terms of the initial modulus of continuity and elapsed time. In particular we characterize those equations for which the Lipschitz constants of solutions can be bounded in terms of their initial oscillation and elapsed time.",

keywords = "Gradient estimate, Quasilinear parabolic equation",

author = "Ben Andrews and Julie Clutterbuck",

year = "2009",

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T1 - Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable

AU - Andrews, Ben

AU - Clutterbuck, Julie

PY - 2009/6/1

Y1 - 2009/6/1

N2 - We bound the modulus of continuity of solutions to quasilinear parabolic equations in one space variable in terms of the initial modulus of continuity and elapsed time. In particular we characterize those equations for which the Lipschitz constants of solutions can be bounded in terms of their initial oscillation and elapsed time.

AB - We bound the modulus of continuity of solutions to quasilinear parabolic equations in one space variable in terms of the initial modulus of continuity and elapsed time. In particular we characterize those equations for which the Lipschitz constants of solutions can be bounded in terms of their initial oscillation and elapsed time.

KW - Gradient estimate

KW - Quasilinear parabolic equation

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U2 - 10.1016/j.jde.2009.01.024

DO - 10.1016/j.jde.2009.01.024

M3 - Article

SN - 0022-0396

VL - 246

SP - 4268

EP - 4283

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 11

ER -

Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable

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