Alternative proof for the existence of Green's function

Pages: 1307 - 1314, Volume 10, Issue 4, July 2011

doi:10.3934/cpaa.2011.10.1307       Abstract        References        Full Text (337.9K)       Related Articles

Sungwon Cho - Department of Mathematics Education, Gwangju National University of Education, 93 Pilmunlo Bugku, Gwangju 500-703, South Korea (email)

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.

Keywords:  Green's function, fundamental solution, second order parabolic equation, Gaussian estimate.
Mathematics Subject Classification:  Primary: 35K10; Secondary: 31B10.

Received: November 2009;      Revised: September 2010;      Published: April 2011.

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