## Second Order Elliptic Equations and Elliptic SystemsThere are two parts to the book. In the first part, a complete introduction of various kinds of a priori estimate methods for the Dirichlet problem of second order elliptic partial differential equations is presented. In the second part, the existence and regularity theories of the Dirichlet problem for linear and nonlinear second order elliptic partial differential systems are introduced. The book features appropriate materials and is an excellent textbook for graduate students. The volume is also useful as a reference source for undergraduate mathematics majors, graduate students, professors, and scientists. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

3 | |

Schauder Theory | 17 |

Lp Theory | 37 |

De GiorgiNashMoser Estimates | 53 |

Quasilinear Equations of Divergence Form | 67 |

KrylovSafonov Estimates | 79 |

Fully Nonlinear Elliptic Equations | 99 |

20 | 111 |

Further regularity and counterexamples | 178 |

27 | 180 |

The reverse Hélder inequality and Lp estimates for | 198 |

33 | 201 |

assess | 204 |

Sobolev Spaces | 209 |

Sards Theorem | 215 |

Proof of the Reverse Hﬁilder Inequality | 225 |

### Other editions - View all

Second Order Elliptic Equations and Elliptic Systems Ya-Zhe Chen,Lan-Cheng Wu No preview available - 1998 |

Second Order Elliptic Equations and Elliptic Systems Yazhe Chen,Lancheng Wu No preview available - 1998 |

### Common terms and phrases

Applying Lemma assume without loss ball Banach space boundary bounded domain bounded linear operator choose converges cubes cutoff function deduce deﬁned Deﬁnition 1.3 denote depends Dirichlet problem divergence form elliptic equations Euler system exists ﬁnd ﬁnite ﬁrst follows Fréchet derivative G Q0 growth condition Harnack inequality Holder estimates Ifu G implies Lebesgue Let Q Let the assumptions Linear Elliptic Systems Math maximum principle method modulus of continuity molliﬁed Morrey natural structure conditions nonlinear elliptic systems nonnegative norm obtain open set Poincaré’s inequality positive constants priori estimate proof is complete prove Q satisﬁes regularity of weak satisﬁes satisfy Schauder theory second order elliptic Sobolev embedding theorem Sobolev space solution of 1.1 solution u G structure conditions F1 subset sufﬁciently Suppose Systems of Divergence Theorem 2.1 valid weak derivatives weak solution x0 G Q