Lorentz estimates for asymptotically regular fully nonlinear parabolic equations | Zendy

Zhang Junjie | Zendy; Zheng Shenzhou | Zendy

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Lorentz estimates for asymptotically regular fully nonlinear parabolic equations

Author(s) -

Zhang Junjie,

Zheng Shenzhou

Publication year - 2018

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201600497

Subject(s) - mathematics , bounded function , nonlinear system , lorentz transformation , hessian matrix , mathematical analysis , class (philosophy) , domain (mathematical analysis) , hessian equation , partial differential equation , physics , classical mechanics , quantum mechanics , artificial intelligence , computer science , first order partial differential equation

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 C 1, 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.

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