Non-quasicontinuous Newtonian functions and outer capacities based on Banach function spaces
Abstract
Abstract We construct various examples of Sobolev-type functions, defined via upper gradients in metric spaces, that fail to be quasicontinuous or weakly quasicontinuous. This is done with quasi-Banach function lattices X as the function spaces defining the smoothness of the Sobolev-type functions. These results are in contrast to the case $$X=L^p$$ X = L p with $$1\le p
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Iterative Methods for Nonlinear Equations
Numerical methods in inverse problems
Publication details
- Journal / source
- Revista Matemática Complutense
- Publication date
- 24 April 2026
- Language
- EN