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arXiv · 1301.1872

Global estimates for nonlinear parabolic equations

Paolo Baroni·Agnese Di Castro·Giampiero Palatucci
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Abstract

We consider nonlinear parabolic equations of the type $$ u_t - div a(x, t, Du)= f(x,t) on \Omega_T = \Omega\times (-T,0), $$ 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.

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Paolo Baroni, Agnese Di Castro, Giampiero Palatucci. 2013-01-09. Global estimates for nonlinear parabolic equations. https://doi.org/10.1007/s00028-013-0174-6

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