Media type: E-Article Title: C1, 1 Regularity in semilinear elliptic problems Contributor: Shahgholian, Henrik Published: Wiley, 2003 Published in: Communications on Pure and Applied Mathematics, 56 (2003) 2, Seite 278-281 Language: English DOI: 10.1002/cpa.10059 ISSN: 1097-0312; 0010-3640 Keywords: Applied Mathematics ; General Mathematics Origination: Footnote: Description: 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.