Memoirs of the American Mathematical Society 2006; 144 pp; softcover Volume: 182 ISBN10: 0821839101 ISBN13: 9780821839102 List Price: US$64 Individual Members: US$38.40 Institutional Members: US$51.20 Order Code: MEMO/182/858
 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. Readership Table of Contents  Introduction
 Modifications of the potential and of onedimensional solutions
 Geometry of the touching points
 Measure theoretic results
 Estimates on the measure of the projection of the contact set
 Proof of Theorem 1.1
 Proof of Theorem 1.2
 Proof of Theorem 1.3
 Proof of Theorem 1.4
 Appendix A. Proof of the measure theoretic results
 Appendix B. Summary of elementary lemmata
 Bibliography
