### Abstract

We prove a Harnack inequality for level sets of p-Laplace phase transition minimizers. In particular, if a level set is included in a fiat cylinder, then, in the interior, it is included in a flatter one. The extension of a result conjectured by De Giorgi and recently proven by the third author for p -2 follows.

Original language | English |
---|---|

Pages (from-to) | 1-150 |

Number of pages | 150 |

Journal | Memoirs of the American Mathematical Society |

Volume | 182 |

Issue number | 858 |

Publication status | Published - 1 Jul 2006 |

Externally published | Yes |

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### Cite this

*Memoirs of the American Mathematical Society*,

*182*(858), 1-150.

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*Memoirs of the American Mathematical Society*, vol. 182, no. 858, pp. 1-150.

**Flat level set regularity of p-Laplace phase transitions.** / Valdinoci, Enrico; Sciunzi, Berardino; Savin, Vasile Ovidiu.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Flat level set regularity of p-Laplace phase transitions

AU - Valdinoci, Enrico

AU - Sciunzi, Berardino

AU - Savin, Vasile Ovidiu

PY - 2006/7/1

Y1 - 2006/7/1

N2 - We prove a Harnack inequality for level sets of p-Laplace phase transition minimizers. In particular, if a level set is included in a fiat cylinder, then, in the interior, it is included in a flatter one. The extension of a result conjectured by De Giorgi and recently proven by the third author for p -2 follows.

AB - We prove a Harnack inequality for level sets of p-Laplace phase transition minimizers. In particular, if a level set is included in a fiat cylinder, then, in the interior, it is included in a flatter one. The extension of a result conjectured by De Giorgi and recently proven by the third author for p -2 follows.

KW - De Giorgi conjecture

KW - Geometric and qualitative properties of solutions

KW - Ginzburg-Landau-Allen-Cahn phase transition models

KW - p-Laplacian operator

KW - Sliding methods

UR - http://www.scopus.com/inward/record.url?scp=33646346403&partnerID=8YFLogxK

M3 - Article

VL - 182

SP - 1

EP - 150

JO - Memoirs of the American Mathematical Society

JF - Memoirs of the American Mathematical Society

SN - 0065-9266

IS - 858

ER -