The Robin boundary conditions represent the flow of a substance or heat through a semi-permeable membrane. Let u be a non-negative solution to the heat equation in a bounded domain with Robin boundary conditions. I will address the question of whether the infimum of u over the whole domain is equal to 0. I will stress the use of probabilistic techniques in the investigation of this purely analytic problem. The talk will be accessible to a broad mathematical audience and graduate students.
Joint work with R. Bass and Z.-Q. Chen.