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Gradient estimates for variable coefficient parabolic equations and singular perturbation problems
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 120, Number 2, April 1998
- pp. 391-439
- 10.1353/ajm.1998.0009
- Article
- Additional Information
In this article we prove, via monotonicity formulas, interior and boundary gradient estimates for solutions to second order parabolic equations, in divergence form, with Dini top order coefficients. We then prove uniform Lipschitz estimates for solutions of singular perturbation problems, using the previous results, and two phase monotonicity formulas.