In this paper we prove a symmetry theorem for the Green function associated to the heat equation in a certain class of bounded domains . For , let and let be the Green function of with pole at . Assume that the adjoint caloric measure in defined with respect to , , is absolutely continuous with respect to a certain surface measure, , on . Our main result states that if
for all and for some , then where is the heat kernel and in . This result has previously been proven by Lewis and Vogel under stronger assumptions on .
Cite this article
John L. Lewis, Kaj Nyström, On a Parabolic Symmetry Problem. Rev. Mat. Iberoam. 23 (2007), no. 2, pp. 513–536DOI 10.4171/RMI/504