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

Malý, J.; Mosco, U.

Ric. Mat. 48, Suppl., 217-231 (1999).

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.

Reviewer: Vladimir Ďurikovič (Bratislava)

MSC:

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

Keywords:

Dirichlet forms; variational fractals; Sobolev inequalities; spaces of homogeneous type; measure-valued Lagrangians; Riesz potential estimates