Poletskiĭ Type Inequality for Mappings from the Orlicz-Sobolev Classes

Abstract

We study the distortion of $$p$$ -module under non-homeomorphic mappings $$f$$ from Orlicz-Sobolev classes $$W^{1,\varphi }_\mathrm{loc}$$ and established a strengthened form of Poletskii’s inequality. This inequality was known for quasiregular mappings and conformal moduli. In addition, our estimates involve the $$p$$ -outer dilatation (instead of the classical inner dilatation) and the multiplicity function. In the case of the planar domains, the condition $$f\in W^{1,\varphi }_\mathrm{loc}$$ can be replaced by $$f\in W^{1,1}_\mathrm{loc}$$ .