Gradient estimates for variable coefficient parabolic equations and singular perturbation problems

American Journal of Mathematics - Tập 120 Số 2 - Trang 391-439 - 1998
Luis Caffarelli, Carlos E. Kenig

Tóm tắt

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.

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