Approximation of continuous functions on a compact set by solutions of elliptic equations. Quantitative results
Journal article, 2026
We establish that a generalized Hölder continuous function on an (m − 2)-Ahlfors regular compact set in ℝm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function.
Author
Grigori Rozenblioum
University of Gothenburg
Chalmers, Mathematical Sciences
Saint Petersburg State University - Spsu
Nikolay Shirokov
Saint Petersburg State University - Spsu
National Research University Higher School of Economics
Israel Journal of Mathematics
0021-2172 (ISSN) 15658511 (eISSN)
Vol. In PressSubject Categories (SSIF 2025)
Computational Mathematics
Mathematical Analysis
DOI
10.1007/s11856-026-2906-7