Introduction and Main Results

This monograph guides readers to mathematical crossroads in heat equations and differential geometry via functional analysis. More precisely, our main purpose is to understand the essence of the Weyl–Hörmander calculus approach of pseudo-differential operators to heat Green operators through concrete calculations for the Dirichlet, Neumann, regular Robin and hypoelliptic Robin boundary conditions, and further to provide better coverage of important examples and applications in elliptic and parabolic problems, being illustrated with many figures and tables.