Functional Analytic Methods for Heat Green Operators: Heat Kernel Asymptotics via the Weyl-H rmander Calculus (Lecture Notes in Mathematics, 2354) free ebook download.

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Functional Analytic Methods for Heat Green Operators: Heat Kernel Asymptotics via the Weyl-H rmander Calculus (Lecture Notes in Mathematics, 2354) free ebook download

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Author(s):	Kazuaki Taira

Date:	2024	Format:	pdf	Language:	English	ISBN/ASIN:	3031666119
Pages:	662	OCR:		Quality:		ISBN13:
Uploader:	alex21s	Upload Date:	9/25/2024 10:12:45 PM

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3031666119 pdf
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 WeylHrmander 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.
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Tags: Analytic Asymptotics Functional Green Heat Heat Kernel Methods Operators Weyl-H

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