An Introduction to Maximum Principles and Symmetry in Elliptic Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Maximum Principles and Symmetry in Elliptic Problems write by L. E. Fraenkel. This book was released on 2000-02-25. An Introduction to Maximum Principles and Symmetry in Elliptic Problems available in PDF, EPUB and Kindle. Advanced text, originally published in 2000, on differential equations, with plentiful supply of exercises all with detailed hints.
Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems
Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems write by Gershon Kresin. This book was released on 2012-08-15. Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems available in PDF, EPUB and Kindle. The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of Miranda-Agmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrix-valued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations.
On Some Applications of the Maximum Principles to a Variety of Elliptic and Parabolic Problems
On Some Applications of the Maximum Principles to a Variety of Elliptic and Parabolic Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Some Applications of the Maximum Principles to a Variety of Elliptic and Parabolic Problems write by Sajan K. Samuel. This book was released on 2019. On Some Applications of the Maximum Principles to a Variety of Elliptic and Parabolic Problems available in PDF, EPUB and Kindle. "One of the most important and useful tools used in the study of partial differential equations is the maximum principle. This principle is a natural extension to higher dimensions of an elementary fact of calculus: any function, which satisfies the inequality f′′ > 0 on an interval [a,b], achieves its maximum at one of the endpoints of the interval. In this context, we say that the solution to the differential inequality f′′ > 0 satisfies a maximum principle. In this thesis we will discuss the maximum principles for partial differential equations and their applications. More precisely, we will show how one may employ the maximum principles to obtain information about uniqueness, approximation, boundedness, convexity, symmetry or asymptotic behavior of solutions, without any explicit knowledge of the solutions themselves. The thesis will be organized in two main parts. The purpose of the first part is to briefly introduce in Chapter 1 the terminology and the main tools to be used throughout this thesis. We will start by introducing the second order linear differential operators of elliptic and parabolic type. Then, we will develop the first and second maximum principles of E. Hopf for elliptic equations, respectively the maximum principles of L. Nirenberg and A. Friedman for parabolic equations. Next, in the second part, namely in Chapter 2 and 3, we will introduce various P-functions, which are nothing else than appropriate functional combinations of the solutions and their derivatives, and derive new maximum principles for such functionals. Moreover, we will show how to employ these new maximum principles to get isoperimetric inequalities, symmetry results and convexity results in the elliptic case (Chapter 2), respectively spatial and temporal asymptotic behavior of solutions, in the parabolic case (Chapter 3)."--Abstract.
Handbook of Differential Equations: Stationary Partial Differential Equations
Handbook of Differential Equations: Stationary Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Handbook of Differential Equations: Stationary Partial Differential Equations write by Michel Chipot. This book was released on 2007-05-03. Handbook of Differential Equations: Stationary Partial Differential Equations available in PDF, EPUB and Kindle. A collection of self contained state-of-the art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching. - written by well-known experts in the field - self contained volume in series covering one of the most rapid developing topics in mathematics
The Maximum Principle
The Maximum Principle - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Maximum Principle write by Patrizia Pucci. This book was released on 2007-12-23. The Maximum Principle available in PDF, EPUB and Kindle. Maximum principles are bedrock results in the theory of second order elliptic equations. This principle, simple enough in essence, lends itself to a quite remarkable number of subtle uses when combined appropriately with other notions. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations.
