## 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 | |

13 | |

The Classical Maximum Principle | 31 |

Poissons Equation and the Newtonian Potential | 51 |

Banach and Hilbert Spaces | 73 |

Classical Solutions the Schauder Approach | 87 |

Sobolev Spaces | 144 |

Generalized Solutions and Regularity | 177 |

Equations in Two Variables | 294 |

Hölder Estimates for the Gradient | 319 |

Boundary Gradient Estimates | 333 |

Global and Interior Gradient Bounds | 359 |

Equations of Mean Curvature Type | 388 |

Fully Nonlinear Equations | 441 |

Bibliography | 491 |

Epilogue | 507 |

Strong Solutions | 219 |

Maximum and Comparison Principles 259 | 260 |

Topological Fixed Point Theorems and Their Application | 279 |

### 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 assume ball Banach space barrier bounded domain BR(y Chapter coefficients compact Consequently converges Corollary defined denote diam Q Dirichlet problem divergence form domain Q Du(x eigenvalues elliptic equations elliptic in Q elliptic operators existence theorem extended follows function u e gradient estimate harmonic functions Harnack inequality hence Hilbert space Hölder continuous Hölder estimate Hölder's inequality hypotheses of Theorem integral interior estimates Lemma Let Q Let u e Let u e C*(Q Lu=f mapping Math matrix maximum principle mean curvature minimal surface Newtonian potential non-negative norms obtain operator Q point xoe Poisson's equation positive constants proof of Theorem Q is elliptic Q satisfies Qu=0 in Q quasilinear equations replaced result second derivatives Section sequence Sobolev Sobolev spaces solution u e solvable strictly elliptic structure conditions subset subsolution sup|ul u e C*(Q unique weak solutions x e Q