Equivalence of solutions for non-homogeneous $ p(x) $-Laplace equations
We establish the equivalence between weak and viscosity solutions for non-homogeneous $ p(x) $-Laplace equations with a right-hand side term depending on the spatial variable, the unknown, CAMPING GEAR and its gradient.We employ inf- and sup-convolution techniques to state that viscosity solutions are also weak solutions, and comparison principles