@article{Medina2023, 
author = {María Medina and Pablo Ochoa},
title = {Equivalence of solutions for non-homogeneous    p  (  x  )-Laplace equations},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {2},
pages = {1-19},
keywords = {nonlinear elliptic equations, p(x)-Laplacian, viscosity solutions, weak solutions, comparison principle},
url = {https://www.sciopen.com/article/10.3934/mine.2023044},
doi = {10.3934/mine.2023044},
abstract = {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, and its gradient. We employ inf- and sup-convolution techniques to state that viscosity solutions are also weak solutions, and comparison principles to prove the converse. The new aspects of the    p  (  x  )-Laplacian compared to the constant case are the presence of    log-terms and the lack of the invariance under translations.}
}