• Medientyp: E-Artikel
  • Titel: C1, 1 Regularity in semilinear elliptic problems
  • Beteiligte: Shahgholian, Henrik
  • Erschienen: Wiley, 2003
  • Erschienen in: Communications on Pure and Applied Mathematics, 56 (2003) 2, Seite 278-281
  • Sprache: Englisch
  • DOI: 10.1002/cpa.10059
  • ISSN: 1097-0312; 0010-3640
  • Schlagwörter: Applied Mathematics ; General Mathematics
  • Entstehung:
  • Anmerkungen:
  • Beschreibung: AbstractIn this paper we give an astonishingly simple proof of C1, 1 regularity in elliptic theory. Our technique yields both new simple proofs of old results as well as new optical results.The setting we'll consider is the following. Let u be a solution to where B, is the unit ball in ℝn, f(x, t) is a bounded Lipschitz function in x, and ft′ is bounded from below. Then we prove that u ⊇ C1, 1 (B1/2). Our method is a simple corollary to a recent monotonicity argument due to Caffarelli, Jerison, and Kenig. © 2002 Wiley Periodicals, Inc.