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• W124493206 abstract "We consider a class of parabolic systems and equations in divergence form modeled by the evolutionary $p$-Laplacean system $$ u_t - operatorname{div} (|Du|^{p-2}Du)=V(x,t) , $$ and provide $L^infty$-bounds for the spatial gradient of solutions $Du$ via nonlinear potentials of the right hand side datum $V$. Such estimates are related to those obtained by Kilpeläinen and Malý [22] in the elliptic case. In turn, the potential estimates found imply optimal conditions for the boundedness of $Du$ in terms of borderline rearrangement invariant function spaces of Lorentz type. In particular, we prove that if $Vin L(n+2,1)$ then $Du in L^infty_{mathrm{loc}}$, where $n$ is the space dimension, and this gives the borderline case of a result of DiBenedetto [5]; a significant point is that the condition $V in L(n+2,1)$ is independent of $p$. Moreover, we find explicit forms of local a priori estimates extending those from [5] valid for the homogeneous case $V equiv 0$." @default.
• W124493206 created "2016-06-24" @default.
• W124493206 creator A5055486184 @default.
• W124493206 creator A5089215657 @default.
• W124493206 date "2012-04-22" @default.
• W124493206 modified "2023-10-10" @default.
• W124493206 title "Potential estimates and gradient boundedness for nonlinear parabolic systems" @default.
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• W124493206 doi "https://doi.org/10.4171/rmi/684" @default.
• W124493206 hasPublicationYear "2012" @default.
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