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In this paper we study a rather wide class of quasilinear parabolic problemswith nonlinear boundary condition and nonstandard growth terms. It includes theimportant case of equations with a $p(t,x)$-Laplacian. By means of thelocalization method and De Giorgi's iteration technique we derive global apriori bounds for weak solutions of such problems. Our results seem to be neweven in the constant exponent case.

Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth