C-1,C-1 regularity in semilinear elliptic problems
2003 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 56, no 2, 278-281 p.Article in journal (Refereed) Published
In this paper we give an astonishingly simple proof of C-1,C-1 regularity in elliptic theory. Our technique yields both new simple proofs of old results as well as new optimal results. The setting we'll consider is the following. Let it be a solution to Deltau = f (x, u) in B, where B is the unit ball in R-n, f (x, t) is a bounded Lipschitz function in x, and f(t)' is bounded from below. Then we prove that u is an element of C-1,C-1 (B-1/2). Our method is a simple corollary to a recent monotonicity argument due to Caffarelli, Jerison, and Kenig.
Place, publisher, year, edition, pages
2003. Vol. 56, no 2, 278-281 p.
IdentifiersURN: urn:nbn:se:kth:diva-22140ISI: 000180052900005OAI: oai:DiVA.org:kth-22140DiVA: diva2:340838
QC 201005252010-08-102010-08-10Bibliographically approved