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Partial differential equations / Jürgen Jost

Main Author Jost, Jürgen, 1956- Country Estados Unidos. Publication New York : Springer, cop. 2002 Description XI, 325 p. ; 24 cm Series Graduate texts in mathematics , 214 ISBN 0-387-95428-7 CDU 517.95
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Holdings
Item type Current location Call number Status Date due Barcode Item holds
Monografia Biblioteca Geral da Universidade do Minho
BGUM 517.95 - J Checked out 2022-12-19 313423
Total holds: 0

Enhanced descriptions from Syndetics:

Intended for students who wish to get an introduction to the theory of partial differential equations, this text focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods and continuity methods. The book 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. Connections between elliptic, parabolic and hyperbolic equations are explored, as well as the connection with Brownian motion and semigroups. This book can be utilized for a one-year course on partial differential equations.

Table of contents provided by Syndetics

  • Introduction
  • The heat equation, semigroups, and Brownian motion
  • The Dirichlet principle
  • Variational methods for the solution of PDE (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
  • Banach and Hilbert spaces
  • The Lp-spaces
  • Bibliography
  • 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 Head equation
  • The wave equation and its connections with the Laplace and heat equation

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