IUMJ

Title: The location of the hot spot in a grounded convex conductor

Authors: Lorenzo Brasco, Rolando Magnanini and Paolo Salani

Issue: Volume 60 (2011), Issue 2, 633-660

Abstract:

We investigate the location of the (unique) hot spot in a convex heat conductor with uniform initial temperature and with boundary grounded at zero temperature. We present two methods to locate the hot spot: the first is based on ideas related to the Alexandrov-Bakelmann-Pucci maximum principle and Monge-Amp\` ere equations; the second relies on Alexandrov's reflection principle. Then we show how such a problem can be simplified in case the conductor is a polyhedron. Finally, we present some numerical computations.