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Remarks on measure-valued Lagrangians on homogeneous spaces. (English) Zbl 0957.46027

The main aim of the authors is to present the proof of Sobolev inequalities on spaces of homogeneous type, for measure-valued Lagrangians that may not have pointwise defined densities (as in the fractal case). The authors use an approach based on Riesz potential estimates.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
31C25 Dirichlet forms
35J70 Degenerate elliptic equations
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