فهرست مطالب
Introduction: What Are Partial Differential Equations?....Pages 1-6
The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order....Pages 7-30
The Maximum Principle....Pages 31-50
Existence Techniques I: Methods Based on the Maximum Principle....Pages 51-75
Existence Techniques II: Parabolic Methods. The Heat Equation....Pages 77-112
The Wave Equation and Its Connections with the Laplace and Heat Equations....Pages 113-125
The Heat Equation, Semigroups, and Brownian Motion....Pages 127-156
The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III)....Pages 157-192
Sobolev Spaces and L 2 Regularity Theory....Pages 193-242
Strong Solutions....Pages 243-254
The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV)....Pages 255-274
The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash....Pages 275-307
The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order....Pages 7-30
The Maximum Principle....Pages 31-50
Existence Techniques I: Methods Based on the Maximum Principle....Pages 51-75
Existence Techniques II: Parabolic Methods. The Heat Equation....Pages 77-112
The Wave Equation and Its Connections with the Laplace and Heat Equations....Pages 113-125
The Heat Equation, Semigroups, and Brownian Motion....Pages 127-156
The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III)....Pages 157-192
Sobolev Spaces and L 2 Regularity Theory....Pages 193-242
Strong Solutions....Pages 243-254
The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV)....Pages 255-274
The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash....Pages 275-307
