A simple proof of the Gaussian lower bound for the Neumann heat kernel of convex domains

Authors

  • M.N. Pascu Transilvania University of Brasov, Romania
  • N.R. Pascu Southern Polytechnic State University, USA
  • M.I. Pop Transilvania University of Brasov, Romania

Keywords:

Neumann heat kernel, Gaussian lower bound, reflecting Brownian motion, mirror coupling of reflecting Brownian motions

Abstract

We present a simple proof of the gaussian lower bound for the Neumann heat kernel of convex domains. The proof is probabilistic in spirit and relies on a geometric property of the extended mirror coupling of reflecting Brownian motions introduced in [7].

Author Biographies

M.N. Pascu, Transilvania University of Brasov, Romania

Department of Mathematics and Computer Science, Str. Iuliu Maniu Nr. 50, Brasov - 500091

N.R. Pascu, Southern Polytechnic State University, USA

Department of Mathematics, 1100 S. Marietta Pkwy, Marietta, GA 30060-2896 

M.I. Pop, Transilvania University of Brasov, Romania

Department of Physics, Str. Colina Universitatii Nr. 1, Brasov - 500091

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Published

2014-01-16

Issue

Vol. 6(55) No. 2 (2013)

Section

MATHEMATICS