# Boundary Behavior of Solutions to Elliptic Equations in General Domains

### Vladimir G. Maz'ya

Linköping University, Sweden and University of Liverpool, UK

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FrontmatterDownload pp. i–v | |

ContentsDownload pp. vii–xi | |

IntroductionDownload pp. 1–5 | |

1 | Behavior near the boundary of solutions to the Dirichlet problem for a second-order elliptic equationpp. 7–66 |

2 | An analogue of theWiener criterion for the Zaremba problem for the Laplacian in a half-cylinderpp. 67–85 |

3 | Wiener type test for the Zaremba problem for degenerate elliptic operators in a half-cylinderpp. 87–112 |

4 | Modulus of continuity of solutions to quasilinear elliptic equationspp. 113–131 |

5 | Discontinuous solution to the $p$-Laplace equationpp. 133–151 |

6 | Wiener test for higher-order elliptic equationspp. 153–190 |

7 | Wiener test for the polyharmonic equationpp. 191–203 |

8 | Weighted positivity andWiener regularity of a boundary point for the fractional Laplacianpp. 205–226 |

9 | Wiener type regularity of a boundary point for the 3D Lamé systempp. 227–245 |

10 | Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equationpp. 257–295 |

11 | Boundedness of derivatives of solutions to the Dirichlet problem for the polyharmonic equationpp. 297–356 |

12 | Polyharmonic capacities and higher-order Wiener testpp. 357–418 |

Bibliographypp. 419–428 | |

General Indexpp. 429–430 | |

Index of Mathematiciansp. 431 |