Author | Jost, Jรผrgen. author |
---|---|
Title | Partial Differential Equations [electronic resource] / by Jรผrgen Jost |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2013 |
Edition | 3rd ed. 2013 |
Connect to | http://dx.doi.org/10.1007/978-1-4614-4809-9 |
Descript | XIII, 410 p. 10 illus. online resource |
Preface -- Introduction: What are Partial Differential Equations? -- 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equation of Second Order -- 2 The Maximum Principle -- 3 Existence Techniques I:ย Methods Based on the Maximum Principle -- 4 Existence Techniques II: Parabolic Methods. The Heat Equation -- 5 Reaction-Diffusion Equations and Systems -- 6 Hyperbolic Equations -- 7 The Heat Equation, Semigroups, and Brownian Motion.-ย 8 Relationshipsย between Different Partial Differential Equations -- 9 Theย Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III) -- 10ย Sobolev Spaces and L̂2 Regularity theory -- 11 Strong solutions -- 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV) -- 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash -- Appendix: Banach and Hilbert spaces. The L̂p-Spaces -- References -- Index of Notation -- Index