Temperatures in Several Variables: Kernel Functions, Representations, and Parabolic Boundary Values

John T. Kemper
1972 Transactions of the American Mathematical Society  
This work develops the notion of a kernel function for the heat equation in certain regions of n +1 -dimensional Euclidean space and applies that notion to the study of the boundary behavior of nonnegative temperatures. The regions in question are bounded between spacelike hyperplanes and satisfy a parabolic Lipschitz condition at points on the lateral boundary. Kernel functions (normalized, nonnegative temperatures which vanish on the parabolic boundary except at a single point) are shown to
more » ... ist uniquely. A representation theorem for nonnegative temperatures is obtained and used to establish the existence of finite parabolic limits at the boundary (except for a set of heat-related measure zero).
doi:10.2307/1996137 fatcat:tkl7oxrgfzhh7allahfr4j445i