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Strongly nonlinear potential theory on metric spaces. (English) Zbl 1017.46022

Sobolev spaces of first order on arbitrary metric spaces attracted some attention in recent times. They are based on related \(L_p\)-spaces. It is the main aim of this paper to replace \(L_p\) by some Orlicz spaces and to develop a corresponding capacity theory.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
31B15 Potentials and capacities, extremal length and related notions in higher dimensions
28A80 Fractals
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