“Mappings of Finite Distortion and PDE with Nonstandard Growth”

Quasiregular mappings with distortion K and solutions of the p-Laplace equation have both been recently extended to the case where the parameter K or p is a function depending on the space variable. For the constant parameter case, results by Bojarski–Iwaniec and Manfredi show that the gradient of a p-harmonic function in the plane is quasiregular or constant. We generalize the result, showing that a planar p(⋅)-harmonic-type function, modeled on the strong equation, is a mapping of finite distortion under appropriate assumptions.