ISBN: 9780521172783

This book presents the basic theory of the symmetry of solutions to second-order elliptic partial differential equations by means of the maximum principle. It proceeds from elementary fac… Meer...

This book presents the basic theory of the symmetry of solutions to second-order elliptic partial differential equations by means of the maximum principle. It proceeds from elementary facts about the linear case to recent results about positive solutions of nonlinear elliptic equations. Gidas, Ni and Nirenberg, building on the work of Alexandrov and Serrin, have shown that the shape of the set on which such elliptic equations are solved has a strong effect on the form of positive solutions. In particular, if the equation and its boundary condition allow spherically symmetric solutions, then, remarkably, all positive solutions are spherically symmetric. These recent and important results are presented with minimal prerequisites, in a style suited to graduate students. Two long appendices give a leisurely account of basic facts about the Laplace and Poisson equations, and there is an abundance of exercises, with detailed hints, some of which contain new results. | An Introduction to Maximum Principles and Symmetry in Elliptic Problems by L. E. Fraenkel Paperback | Indigo Chapters Books > Science & Nature > Math & Physics > Mathematics > Mathematical Analysis P10117, L. E. Fraenkel<

ISBN: 9780521172783

This book presents the basic theory of the symmetry of solutions to second-order elliptic partial differential equations by means of the maximum principle. It proceeds from elementary fac… Meer...

This book presents the basic theory of the symmetry of solutions to second-order elliptic partial differential equations by means of the maximum principle. It proceeds from elementary facts about the linear case to recent results about positive solutions of nonlinear elliptic equations. Gidas, Ni and Nirenberg, building on the work of Alexandrov and Serrin, have shown that the shape of the set on which such elliptic equations are solved has a strong effect on the form of positive solutions. In particular, if the equation and its boundary condition allow spherically symmetric solutions, then, remarkably, all positive solutions are spherically symmetric. These recent and important results are presented with minimal prerequisites, in a style suited to graduate students. Two long appendices give a leisurely account of basic facts about the Laplace and Poisson equations, and there is an abundance of exercises, with detailed hints, some of which contain new results. Books > Science & Nature > Math & Physics > Mathematics > Mathematical Analysis List_Books, [PU: Cambridge University Press]<

2000, ISBN: 9780521172783

Paperback, [PU: Cambridge University Press], The author of this 2000 volume proceeds from elementary facts about the linear case to recent results about positive solutions of non-linear e… Meer...

Paperback, [PU: Cambridge University Press], The author of this 2000 volume proceeds from elementary facts about the linear case to recent results about positive solutions of non-linear elliptic equations, with minimal prerequisites in a style suited to graduate students. There is a plentiful supply of exercises, with detailed hints, some of which contain new results., Differential Calculus & Equations<

2010, ISBN: 0521172780

Kartoniert / Broschiert MATHEMATICS / Differential Equations / Partial, mit Schutzumschlag 11, [PU:Cambridge University Press]

2011, ISBN: 9780521172783

Buch, Softcover, [PU: Cambridge University Press], Cambridge University Press, 2011