Global gradient estimates for parabolic equations with measurable nonlinearities

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Abstract

We establish a global Calderón–Zygmund theory of nonlinear parabolic equations with measurable nonlinearities in divergence form by proving that the spatial gradient of a weak solution is as integrable as the inhomogeneous term. Nonlinearity a(ξ,x,t) is assumed to be only measurable in one spatial variable and has locally small BMO semi-norm in the other spatial and time variables, uniformly with respect to ξ variable. The boundary of the bounded domain can be beyond the Lipschitz category, but it is well trapped in two narrow strips at each point and at each scale.

Original languageEnglish
Pages (from-to)77-99
Number of pages23
JournalNonlinear Analysis, Theory, Methods and Applications
Volume164
DOIs
StatePublished - Nov 2017

Keywords

  • Calderón–Zygmund type estimate
  • Measurable nonlinearity
  • Nonlinear parabolic equation
  • Reifenberg flat domain

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