Lorentz estimates for asymptotically regular fully nonlinear parabolic equations

Junjie Zhang and Shenzhou Zheng

Mathematische Nachrichten, 2018, vol. 291, issue 5-6, 996-1008

Abstract: We prove a global Lorentz estimate of the Hessian of strong solutions to the Cauchy–Dirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded C1, 1 domain. Here, we mainly assume that the associated regular nonlinearity satisfies uniformly parabolicity and the (δ,R)†vanishing condition, and the approach of constructing a regular problem by an appropriate transformation is employed.

Date: 2018
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