Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2007; 44(3): 585-603

Printed May 1, 2007

Copyright © The Korean Mathematical Society.

Holder convergence of the weak solution to an evolution equation of $p$-Ginzburg-Landau type

Yutian Lei

Nanjing Normal University

Abstract

The author studies the local H\"older convergence of the solution to an evolution equation of $p$-Ginzburg-Landau type, to the heat flow of the $p$-harmonic map, when the parameter tends to zero. The convergence is derived by establishing a uniform gradient estimation for the solution of the regularized equation.

Keywords: Holder convergence, $p$-Ginzburg-Landau equations, heat flow of $p$-harmonic map

MSC numbers: 35B25, 35K55, 35K65

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