Functional Analytic Methods for Heat Green Operators

Beschreibung

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–Hörmander 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.

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–Hörmander 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.

Autor*in

Kazuaki Taira

Themen in »Functional Analytic Methods for Heat Green Operators«

Heat Green Operator Hypoelliptic Robin Problem Heat Kernel Asymptotics Weyl--Hörmander Calculus Analytic Semigroup Partial Differential Equations Partial Differential Equations on Manifolds

Stimmen zu »Functional Analytic Methods for Heat Green Operators«

“The book is very carefully written, and the explanation of the main ideas is always given to clarify the methods and steps. It is a very valuable and useful contribution for scholars in the field and researchers who wish to get an idea of methods and problems related to heat kernel asymptotics for boundary value problems.” (Alberto Parmeggiani, Mathematical Reviews, October, 2025) 

Details

Link teilen