Abstract
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.
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