偏微分方程式（第２版） Partial Differential Equations (Graduate Texts in Mathematics) 〈Vol. 214〉 （2ND）

Jost, Jürgen

Springer（2007/03発売）

• 製本 Hardcover:ハードカバー版／ページ数 356 p.／サイズ 10 illus.
• 言語 ENG
• 商品コード 9780387493183

基本説明

Focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. Several additions have been made to the 2nd edition, including a new chapter on Reacition-diffusion equations.

Full Description

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.

Contents

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.