## Elliptic Partial Differential Equations of Second OrderFrom the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures". Newsletter, New Zealand Mathematical Society, 1985 "Primarily addressed to graduate students this elegant book is accessible and useful to a broad spectrum of applied mathematicians". Revue Roumaine de Mathématiques Pures et Appliquées,1985 |

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### Contents

1 | |

8 | |

13 | |

16 | |

The Classical Maximum Principle | 31 |

Poissons Equation and the Newtonian Potential | 51 |

Banach and Hilbert Spaces | 73 |

Classical Solutions the Schauder Approach | 87 |

Fully Nonlinear Equations | 266 |

Topological Fixed Point Theorems and Their Application | 279 |

Equations in Two Variables | 294 |

Chapter 13 Hölder Estimates for the Gradient | 319 |

Boundary Gradient Estimates | 333 |

Global and Interior Gradient Bounds | 359 |

Bibliography | 491 |

Epilogue | 507 |

Sobolev Spaces | 144 |

Strong Solutions | 219 |

Maximum and Comparison Principles | 259 |

### Other editions - View all

Elliptic Partial Differential Equations of Second Order David Gilbarg,Neil S. Trudinger Limited preview - 2001 |

Elliptic Partial Differential Equations of Second Order D. Gilbarg,Neil Trudinger No preview available - 2014 |

### Common terms and phrases

apply arbitrary argument assert assume ball Banach space barrier boundary values bounded bounded domain called Chapter choose classical coefficients compact condition Consequently consider constant contained converges convex Corollary corresponding curvature defined denote depending derivatives differentiable Dirichlet problem dist divergence domain Q elliptic equations equivalent established estimate example existence extended exterior fixed follows function given global gradient hence Hölder estimate holds hypotheses implies independent inequality integral Lemma Let Q Let u e linear mapping maximum principle mean method norms obtain operator particular positive constants potential preceding proof proof of Theorem prove regularity Remark replaced respect result satisfies sequence smooth ſº solution solvability subset sufficiently suppose surface Theorem theory u e C*(Q uniformly elliptic unique valid weak write