Alternative proof for the existence of Green's function
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.
Received: November 2009; Revised: September 2010; Published: April 2011.
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