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Book
Nonelliptic partial differential equations : analytic hypoellipticity and the courage to localize high powers of T
Author:
ISBN: 1441998128 1441998136 Year: 2011 Publisher: New York : Springer,

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Abstract

This book fills a real gap in the analytical literature. After many years and many results of analytic regularity for partial differential equations, the only access to the technique known as $(T^p)_phi$ has remained embedded in the research papers themselves, making it difficult for a graduate student or a mature mathematician in another discipline to master the technique and use it to advantage. This monograph takes a particularly non-specialist approach, one might even say gentle, to smoothly bring the reader into the heart of the technique and its power, and ultimately to show many of the results it has been instrumental in proving. Another technique developed simultaneously by F. Treves is developed and compared and contrasted to ours.   The techniques developed here are tailored to proving real analytic regularity to solutions of sums of squares of vector fields with symplectic characteristic variety and others, real and complex. The motivation came from the field of several complex variables and the seminal work of J. J. Kohn. It has found application in non-degenerate (strictly pseudo-convex) and degenerate situations alike, linear and non-linear, partial and pseudo-differential equations, real and complex analysis. The technique is utterly elementary, involving powers of vector fields and carefully chosen localizing functions. No knowledge of advanced techniques, such as the FBI transform or the theory of hyperfunctions is required. In fact analyticity is proved using only $C^infty$ techniques.   The book is intended for mathematicians from graduate students up, whether in analysis or not, who are curious which non-elliptic partial differential operators have the property that all solutions must be real analytic. Enough background is provided to prepare the reader with it for a clear understanding of the text, although this is not, and does not need to be, very extensive. In fact, it is very nearly true that if the reader is willing to accept the fact that pointwise bounds on the derivatives of a function are equivalent to bounds on the $L^2$ norms of its derivatives locally, the book should read easily.


Book
Progress on meshless methods
Authors: --- --- ---
ISBN: 1402088205 9048179971 9786611913496 1281913499 1402088213 Year: 2009 Publisher: Dordrecht : Springer Science,

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Abstract

In recent years meshless/meshfree methods have gained considerable attention in engineering and applied mathematics. The variety of problems that are now being addressed by these techniques continues to expand and the quality of the results obtained demonstrates the effectiveness of many of the methods currently available. The book presents a significant sample of the state of the art in the field with methods that have reached a certain level of maturity while also addressing many open issues. The book collects extended original contributions presented at the Second ECCOMAS Conference on Meshless Methods held in 2007 in Porto. The list of contributors reveals a fortunate mix of highly distinguished authors as well as quite young but very active and promising researchers, thus giving the reader an interesting and updated view of different meshless approximation methods and their range of applications. The material presented is appropriate for researchers, engineers, physicists, applied mathematicians and graduate students interested in this active research area.

Keywords

Finite element method -- Congresses. --- Finite element method. --- Meshfree methods (Numerical analysis) -- Congresses. --- Meshfree methods (Numerical analysis). --- Meshfree methods (Numerical analysis) --- Finite element method --- Engineering & Applied Sciences --- Applied Mathematics --- Engineering - General --- Mathematical analysis. --- Gridless methods (Numerical analysis) --- Meshfree discretization techniques (Numerical analysis) --- Meshless methods (Numerical analysis) --- 517.1 Mathematical analysis --- Mathematical analysis --- Engineering. --- Computer-aided engineering. --- Computer mathematics. --- Numerical analysis. --- Applied mathematics. --- Engineering mathematics. --- Computational intelligence. --- Engineering, general. --- Numerical Analysis. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Appl.Mathematics/Computational Methods of Engineering. --- Computational Intelligence. --- Computational Mathematics and Numerical Analysis. --- Intelligence, Computational --- Artificial intelligence --- Engineering --- Engineering analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- CAE --- Construction --- Industrial arts --- Technology --- Mathematics --- Data processing --- Soft computing --- Numerical analysis --- Computer aided design. --- Computer science --- Mathematical and Computational Engineering. --- Mathematics. --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design

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