An obstacle problem and superharmonic functions with nonstandard growth

In this article we study solutions and supersolutions of a variable exponent p(⋅)p(⋅)-Laplace equation, and the corresponding obstacle problem, as well as related p(⋅)p(⋅)-superharmonic functions. The relationship between these function classes closely parallels the classical case. However, integrability properties of p(⋅)p(⋅)-superharmonic functions require stronger assumptions.