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$L_∞$-estimate for solutions of nonlinear parabolic systems

Tom 33 / 1996

Wojciech Zajączkowski 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.

Autorzy

  • Wojciech Zajączkowski

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