$L_∞$-estimate for solutions of nonlinear parabolic systems
Tom 33 / 1996
Banach Center Publications 33 (1996), 465-490
DOI: 10.4064/-33-1-465-490
Streszczenie
We prove existence of weak solutions to nonlinear parabolic systems with p-Laplacians terms in the principal part. Next, in the case of diagonal systems an $L_∞$-estimate for weak solutions is shown under additional restrictive growth conditions. Finally, $L_∞$-estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The $L_∞$-estimates are obtained by the Di Benedetto methods.
