In the present paper, we prove existence results of entropy solutions to a class of nonlinear degenerate parabolic p(·)-Laplacian problem with Dirichlet-type boundary conditions and L1 data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.
In this paper, we prove the existence and uniqueness results of entropy solution to a class of nonlinear degenerate elliptic problem with Dirichlet-type boundary condition and L1 data. The main tool used here is the regularization approach combined with theory of weighted Sobolev spaces.