@article{Cruz-Uribe2022, 
author = {David Cruz-Uribe and Michael Penrod and Scott Rodney},
title = {Poincaré inequalities and Neumann problems for the variable exponent setting},
year = {2022},
journal = {Mathematics in Engineering},
volume = {4},
number = {5},
pages = {1-22},
keywords = {degenerate Sobolev spaces, p-Laplacian, Poincaréinequalities, variable exponent, nonstandard growth conditions},
url = {https://www.sciopen.com/article/10.3934/mine.2022036},
doi = {10.3934/mine.2022036},
abstract = {In an earlier paper, Cruz-Uribe, Rodney and Rosta proved an equivalence between weighted Poincaré inequalities and the existence of weak solutions to a family of Neumann problems related to a degenerate    p-Laplacian. Here we prove a similar equivalence between Poincaré inequalities in variable exponent spaces and solutions to a degenerate        p    (    ⋅    )  -Laplacian, a non-linear elliptic equation with nonstandard growth conditions.}
}