Approximation of continuous functions on a compact set by solutions of elliptic equations. Quantitative results
Abstract
Abstract We establish that a generalized Hölder continuous function on an (m−2)-Ahlfors regular compact set K in Rm can be uniformly on K approximated by solutions of a second order elliptic equation with mildly regular coefficients, with the rate of the approximation and the quality of the approximating function determined by the continuity modulus of the function.
Fields of Study & Subjects
Mathematical Approximation and Integration
Advanced Mathematical Modeling in Engineering
Mathematical functions and polynomials
Publication details
- Journal / source
- Israel Journal of Mathematics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 274
- Issue
- 1
- Pages
- 89–118
- Publication date
- 6 April 2026
- Language
- EN