Alternative proof for the existence of Green's function

Sungwon Cho

doi:10.3934/cpaa.2011.10.1307

Article Contents

2011, Volume 10, Issue 4: 1307-1314. Doi: 10.3934/cpaa.2011.10.1307

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Alternative proof for the existence of Green's function

Sungwon Cho^1,

1.
Department of Mathematics Education, Gwangju National University of Education, 93 Pilmunlo Bugku, Gwangju 500-703

Received: October 31, 2009

Revised: August 31, 2010

Published: June 2011

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Abstract

We present a new method for the existence of a Green's function of nod-divergence form parabolic operator with Hölder continuous coefficients. We also derive a Gaussian estimate. Main ideas involve only basic estimates and known results without a potential approach, which is used by E.E. Levi.

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Mathematics Subject Classification: Primary: 35K10; Secondary: 31B10.

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