STRONGLY NONLINEAR POTENTIAL THEORY ON METRIC SPACES

We define Orlicz-Sobolev spaces on an arbitrary metric space with a Borel reg-ular outer measure, and we develop a capacity theory based on these spaces. We study basic properties of capacity and several convergence results. We prove that each Orlicz-Sobolev function has a quasi-continuous representative. We give es-timates for the capacity of balls when the measure is doubling. Under additional regularity assumption on the measure, we establish some relations between ca-pacity and Hausdorffmeasures. 1