Potential Theory

This book presents a clear path from calculus to classical potential theory and beyond with the aim of moving the reader into a fertile area of mathematical research as quickly as possible. The first half of the book develops the subject matter from first principles using only calculus. The second half comprises more advanced material for those with a senior undergraduate or beginning graduate course in real analysis. For specialized regions, solutions of Laplace's equation are constructed having prescribed normal derivatives on the flat portion of the boundary and prescribed values on the remaining portion of the boundary. By means of transformations known as diffeomorphisms, these solutions are morphed into local solutions on regions with curved boundaries. The Perron-Weiner-Brelot method is then used to construct global solutions for elliptic PDEs involving a mixture of prescribed values of a boundary differential operator on part of the boundary and prescribed values on the remainder of the boundary.

ISBN 1848823185   Volumes 1 ISBN13 9781848823181 (What's this?)   Weight (grammes) 635 Publisher Springer London Ltd   Published in England Imprint Springer London Ltd   Series title Universitext Format Paperback   Height (mm) 234 Publication date 01 Jun 2009   Width (mm) 156 DEWEY 515.96   Spine width (mm) 23 DEWEY edition DC22   Academic level Professional / Scholarly Pages 456

0		Preliminaries		1
1		Laplace's equation		7
2		The Dirichlet problem		53
3		Green functions		107
4		Negligible sets		149
5		Dirichlet problem for unbounded regions		197
6		Energy		241
7		Interpolation and monotonicity		267
8		Newtonian potential		303
9		Elliptic operators		333
10		Apriori bounds		371
11		Oblique derivative problem		391
		References		431
		Index		435
		Notation		439

From the reviews: "The author sets the goal of the book as getting the reader from real analysis to the front line of potential theory as quickly as possible. ! Each chapter begins with some physical and historical context ! . The excellent index is also very helpful in navigating the material. ! a fine text for self-study, reference, or a graduate course. Researchers in the field will consider it a standard and those in an adjacent field ! will also find it a valuable reference." (Bill Wood, The Mathematical Association of America, May, 2010) "The first part of the book deals with the basics of classical potential theory while the rest of the book deals with the solution to elliptic partial differential equations with various boundary conditions. ! Proofs are given in easy to follow detail. ! the book is very suitable as a textbook ! . On the whole, this book is a very useful addition to available resources. ! There is also an index, a notation guide and an extensive bibliography." (P. Lappan, Mathematical Reviews, Issue 2011 a)

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