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Flat Level Set Regularity of p-Laplace Phase Transitions illustrated Edition [Minkštas viršelis]

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  • Formatas: Paperback / softback, 144 pages, weight: 312 g, illustrations
  • Serija: Memoirs of the American Mathematical Society
  • Išleidimo metai: 01-Jul-2006
  • Leidėjas: American Mathematical Society
  • ISBN-10: 0821839101
  • ISBN-13: 9780821839102
Kitos knygos pagal šią temą:
Flat Level Set Regularity of p-Laplace Phase Transitions illustrated EditionDidesnis paveikslėlis
  • Formatas: Paperback / softback, 144 pages, weight: 312 g, illustrations
  • Serija: Memoirs of the American Mathematical Society
  • Išleidimo metai: 01-Jul-2006
  • Leidėjas: American Mathematical Society
  • ISBN-10: 0821839101
  • ISBN-13: 9780821839102
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780821839102.html
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.
Introduction
1(6)
Modifications of the potential and of one-dimensional solutions
7(24)
Geometry of the touching points
31(12)
Measure theoretic results
43(4)
Estimates on the measure of the projection of the contact set
47(14)
Proof of Theorem 1.1
61(8)
Proof of Theorem 1.2
69(6)
Proof of Theorem 1.3
75(4)
Proof of Theorem 1.4
79(4)
Appendix A. Proof of the measure theoretic results
83(52)
Proof of Lemma 4.1
83(5)
Proof of Lemma 4.2
88(39)
Proof of Lemma 4.3
127(8)
Appendix B. Summary of elementary lemmata
135(8)
Bibliography 143