Functional Analytic Methods for Heat Green Operators

<p>This monograph guides the reader to the mathematical crossroads of heat equations and differential geometry via functional analysis.  Following the recent trend towards constructive methods in the theory of partial differential equations it makes extensive use of the ideas and techniques from the Weyl���H��rmander calculus of pseudo-differential operators to study heat Green operators through concrete calculations for the Dirichlet Neumann regular Robin and hypoelliptic Robin boundary conditions. Further it provides detailed coverage of important examples and applications in elliptic and parabolic problems illustrated with many figures and tables. A unified mathematical treatment for solving initial boundary value problems for the heat equation under general Robin boundary conditions is desirable and leads to an extensive study of various aspects of elliptic and parabolic partial differential equations. The principal ideas are explicitly presented so that a broad spectrum of readers can easily understand the problem and the main results. The book will be of interest to readers looking for a functional analytic introduction to the meeting point of partial differential equations differential geometry and probability.</p>