A gradient estimate for solutions to parabolic equations with discontinuous coefficients

Title
A gradient estimate for solutions to parabolic equations with discontinuous coefficients
Authors
나까무라
Keywords
Parabolic equations; discontinuous coe cients; gradient estimate
Issue Date
2013
Publisher
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
Series/Report no.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS ; Vol2013 no.93 Startpage 1 Endpage 24
Abstract
Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be given by manifolds of codimension 1, which we called them manifolds of discontinuities. Their gradient estimate is independent of the distances between manifolds of discontinuities. In this paper, we gave a parabolic version of their results. That is, we gave a gradient estimate for parabolic equations of divergence forms with piecewise smooth coefficients. The coef- ficients are assumed to be independent of time and their discontinuities are likewise the previous elliptic equations. As an application of this estimate, we also gave a pointwise gradient estimate for the fundamental solution of a parabolic operator with piecewise smooth coefficients. Both gradient estimates are independent of the distances between manifolds of discontinuities.
URI
http://dspace.inha.ac.kr/handle/10505/33364
ISSN
1072-6691
Appears in Collections:
College of Natural Science(자연과학대학) > Mathematics (수학) > Local Access Journal Papers, Reports(수학 논문, 보고서)

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