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Flat Level Set Regularity of $p$-Laplace Phase Transitions
| eBook ISBN: | 978-1-4704-0462-8 |
| Product Code: | MEMO/182/858.E |
| List Price: | $68.00 |
| MAA Member Price: | $61.20 |
| AMS Member Price: | $40.80 |
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Flat Level Set Regularity of $p$-Laplace Phase Transitions
| eBook ISBN: | 978-1-4704-0462-8 |
| Product Code: | MEMO/182/858.E |
| List Price: | $68.00 |
| MAA Member Price: | $61.20 |
| AMS Member Price: | $40.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 182; 2006; 144 ppMSC: Primary 35
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
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Chapters
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1. Introduction
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2. Modifications of the potential and of one-dimensional solutions
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3. Geometry of the touching points
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4. Measure theoretic results
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5. Estimates on the measure of the projection of the contact set
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6. Proof of Theorem 1.1
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7. Proof of Theorem 1.2
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8. Proof of Theorem 1.3
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9. Proof of Theorem 1.4
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Volume: 182; 2006; 144 pp
MSC: Primary 35
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
-
Chapters
-
1. Introduction
-
2. Modifications of the potential and of one-dimensional solutions
-
3. Geometry of the touching points
-
4. Measure theoretic results
-
5. Estimates on the measure of the projection of the contact set
-
6. Proof of Theorem 1.1
-
7. Proof of Theorem 1.2
-
8. Proof of Theorem 1.3
-
9. Proof of Theorem 1.4
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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