Journal of Evolution Equations

, Volume 13, Issue 1, pp 163–195 | Cite as

Global estimates for nonlinear parabolic equations

  • Paolo Baroni
  • Agnese Di Castro
  • Giampiero Palatucci
Article

Abstract

We consider nonlinear parabolic equations of the type
$$u_t - {\rm div}a(x, t, Du)= f(x, t) \quad {\rm on}\quad \Omega_T =\Omega\times (-T,0),$$
under standard growth conditions on a, with f only assumed to be integrable. We prove general decay estimates up to the boundary for level sets of the solutions u and the gradient Du which imply very general estimates in Lebesgue and Lorentz spaces. Assuming only that the involved domains satisfy a mild exterior capacity density condition, we provide global regularity results.

Mathematics Subject Classification (2000)

35K55 35B65 35K10 46E30 

Keywords

Nonlinear parabolic problems Calderón-Zygmund theory Lorentz regularity Rearrangement invariant function spaces Higher integrability 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Paolo Baroni
    • 1
  • Agnese Di Castro
    • 2
  • Giampiero Palatucci
    • 2
  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità degli Studi di ParmaParmaItaly

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