We prove boundedness of the weak solutions to the Cauchy–Dirichlet problem for quasilinear parabolic equations whose prototype is the parabolic m-Laplacian. The nonlinear terms satisfy sub-controlled growth conditions with respect to the unknown function and its spatial gradient, while the behaviour in the independent variables is modelled in Lebesgue–Morrey spaces.
Boundedness of solutions to quasilinear parabolic equations
Palagachev, D. K.;
2016-01-01
Abstract
We prove boundedness of the weak solutions to the Cauchy–Dirichlet problem for quasilinear parabolic equations whose prototype is the parabolic m-Laplacian. The nonlinear terms satisfy sub-controlled growth conditions with respect to the unknown function and its spatial gradient, while the behaviour in the independent variables is modelled in Lebesgue–Morrey spaces.File in questo prodotto:
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