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

Format:

Book

Author/Creator:

Valdinoci, Enrico, 1974- author.

Sciunzi, Berardino, author.

Savin, Vasile Ovidiu, 1977- author.

Series:

Memoirs of the American Mathematical Society ; no. 858.

Memoirs of the American Mathematical Society, 0065-9266 ; number 858

Language:

English

Subjects (All):

Geometry, Differential.

Laplacian operator.

Level set methods.

Physical Description:

1 online resource (158 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2006]

Language Note:

English

Summary:

We prove a Harnack inequality for level sets of $p$-Laplace phase transition minimizers. In particular, if a level set is included in a flat 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.

Contents:

""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Modifications of the potential and of one-dimensional solutions""; ""Chapter 3. Geometry of the touching points""; ""Chapter 4. Measure theoretic results""; ""Chapter 5. Estimates on the measure of the projection of the contact set""; ""Chapter 6. Proof of Theorem 1.1""; ""Chapter 7. Proof of Theorem 1.2""; ""Chapter 8. Proof of Theorem 1.3""; ""Chapter 9. Proof of Theorem 1.4""; ""Appendix A. Proof of the measure theoretic results""; ""A.1. Proof of Lemma 4.1""; ""A.2. Proof of Lemma 4.2""; ""A.3. Proof of Lemma 4.3""

""Appendix B. Summary of elementary lemmata""""Bibliography""

Notes:

"July 2006, volume 182, number 858 (second of 4 numbers)."

Includes bibliographical references (pages 143-144).

Description based on print version record.

ISBN:

1-4704-0462-1