Journal article
C0-regularity for solutions of elliptic equations with distributional coefficients
Journal of Differential Equations, Vol.470, 114389
07/25/2026
DOI: 10.1016/j.jde.2026.114389
Abstract
In this paper, the continuity of solutions for elliptic equations in divergence form with distributional coefficients is considered. Inspired by the discussion on necessary and sufficient conditions for the form boundedness of elliptic operators by Maz'ya and Verbitsky (Acta Math. 188 (2002) 263-302 and Commun. Pure Appl. Math. 59 (2006), 1286-1329), we propose two kinds of sufficient conditions, which are some Dini decay conditions and some integrable conditions named Kato class or K1 class, to show that the weak solution of the Schrödinger type elliptic equation with distributional coefficients is continuous, and give a priori estimate which is almost optimal. These estimates can clearly show that how the coefficients and nonhomogeneous terms influence the regularity of solutions. The ln-Lipschitz regularity and Hölder regularity are also obtained as corollaries which cover the classical De Giorgi's Hölder estimates.
Details
- Title: Subtitle
- C0-regularity for solutions of elliptic equations with distributional coefficients
- Creators
- Jingqi Liang - Shanghai Jiao Tong UniversityLihe Wang - University of IowaChunqin Zhou - Shanghai Jiao Tong University
- Resource Type
- Journal article
- Publication Details
- Journal of Differential Equations, Vol.470, 114389
- DOI
- 10.1016/j.jde.2026.114389
- ISSN
- 0022-0396
- eISSN
- 1090-2732
- Publisher
- Elsevier; SAN DIEGO
- Grant note
- Natural Science Foundation of Shanghai: 24ZR1440700 Fundamental Research Funds for the Central Universities: B250201283 National Natural Science Foundation of China: 12031012
The first author was partially supported by Natural Science Foundation of Shanghai Grant 24ZR1440700 and supported by Fundamental Research Funds for the Central Universities Grant B250201283. The third author was partially supported by National Natural Science Foundation of China Grant 12031012 and Natural Science Foundation of Shanghai Grant 24ZR1440700.
- Language
- English
- Electronic publication date
- 04/15/2026
- Date published
- 07/25/2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985157616102771
Metrics
1 Record Views