GRADIENT ESTIMATES FOR VARIABLE-COEFFICIENT PARABOLIC EQUATIONS AND SINGULAR PERTURBATION PROBLEMS

Authors
CAFFARELLI LA KENIG CE
Citation
La. Caffarelli et Ce. Kenig, GRADIENT ESTIMATES FOR VARIABLE-COEFFICIENT PARABOLIC EQUATIONS AND SINGULAR PERTURBATION PROBLEMS, American journal of mathematics, 120(2), 1998, pp. 391-439
Citations number
20
Categorie Soggetti
Mathematics,Mathematics
Journal title
American journal of mathematics → ACNP
ISSN journal
00029327
Volume
120
Issue
2
Year of publication
1998
Pages
391 - 439
Database
ISI
SICI code
0002-9327(1998)120:2<391:GEFVPE>2.0.ZU;2-0
Abstract
In this article we prove, via monotonicity formulas, interior and boun dary gradient estimates for solutions to second order parabolic equati ons, in divergence form, with Dini top order coefficients. We then pro ve uniform Lipschitz estimates for solutions of singular perturbation problems, using the previous results, and two phase monotonicity formu las.