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.


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