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Lorentz estimates for asymptotically regular fully nonlinear parabolic equations

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  • Junjie Zhang
  • Shenzhou Zheng

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.

Suggested Citation

  • Junjie Zhang & Shenzhou Zheng, 2018. "Lorentz estimates for asymptotically regular fully nonlinear parabolic equations," Mathematische Nachrichten, Wiley Blackwell, vol. 291(5-6), pages 996-1008, April.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:5-6:p:996-1008
    DOI: 10.1002/mana.201600497
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    Cited by:

    1. Shuang Liang & Shenzhou Zheng, 2023. "Gradient estimate for asymptotically regular elliptic equations of double phase with variable exponents," Mathematische Nachrichten, Wiley Blackwell, vol. 296(2), pages 701-715, February.

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