热格林算子的泛函分析方法：基于Weyl-Hormander演算的热核渐近性

English | 2024 | ASIN: B0DGDPSGH3 | 662 pages | Epub PDF (True) | 77 MB

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.

英文|2024|ASIN:B0DGDPSGH3|662页|Epub PDF（真）|77 MB 这本专著通过泛函分析将读者引导到热方程和微分几何的数学十字路口。随着偏微分方程理论中构造方法的最新趋势，它广泛利用伪微分算子Weyl-Hormander演算的思想和技术，通过对Dirichlet、Neumann、正则Robin和次椭圆Robin边界条件的具体计算来研究热格林算子。此外，它还详细介绍了椭圆和抛物线问题中的重要示例和应用，并用许多图表进行了说明。在一般Robin边界条件下，求解热方程初边值问题的统一数学处理是可取的，这导致了对椭圆和抛物线偏微分方程各个方面的广泛研究。主要观点被明确地呈现出来，以便广大读者能够轻松理解问题和主要结果。这本书将吸引那些希望对偏微分方程、微分几何和概率的交点进行泛函分析介绍的读者。

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