$L_∞$-estimates for solutions of nonlinear parabolic systems with gradient linear growth
Volume 33 / 1996
Banach Center Publications 33 (1996), 491-501
DOI: 10.4064/-33-1-491-501
Abstract
Existence of weak solutions and an $L_∞$-estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The $L_∞$-estimate is proved for equations with coefficients continuous with respect to x and t in the general main part, and for diagonal systems with coefficients satisfying the Carathéodory condition.
