Jürgen Jost
Springer New York
2e druk, 2010
9781441923806
Partial Differential Equations
Specificaties
Paperback, 356 blz.
|
Engels
Springer New York |
2e druk, 2010
ISBN13: 9781441923806
Rubricering
Onderdeel van serie
Graduate Texts in Mathematics
Levertijd ongeveer 8 werkdagen
Samenvatting
This book offers an ideal introduction to the theory of partial differential equations. It focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. It also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. It also explores connections between elliptic, parabolic, and hyperbolic equations as well as the connection with Brownian motion and semigroups. This second edition features a new chapter on reaction-diffusion equations and systems.
Specificaties
ISBN13:9781441923806
Taal:Engels
Bindwijze:paperback
Aantal pagina's:356
Uitgever:Springer New York
Druk:2
Inhoudsopgave
Preface to the First Edition.- Preface to the Second Edition.- Introduction.- The Laplace equation as the prototype of an elliptic partial differential equation of 2nd order.- The maximum principle.- Existence techniques I: methods based on the maximum principle.- Existence techniques II: Parabolic methods. The Heat equation.- Reaction Diffusion Equations and Systems.- The wave equation and its connections with the Laplace and heat equations * The heat equation, semigroups, and Brownian motion * The Dirichlet principle. Variational methods for the solution of PDEs (Existence techniques III) * Sobolev spaces and L2 regularity theory * Strong solutions * The regularity theory of Schauder and the continuity method (Existence techniques IV) * The Moser iteration method and the reqularity theorem of de Giorgi and Nash * Appendix: Banach and Hilbert spaces. The Lp-spaces.- References.- Index of Notation.- Index.-