Regularity and explicit L∞ estimates for a class of nonlinear elliptic systems
We use De Giorgi-Nash-Moser iteration scheme to establish that weak solutions to a coupled system of elliptic equations with critical growth on the boundary are in L ∞ (Ω). Moreover, we provide an explicit L ∞ (Ω)- estimate of weak solutions with subcritical growth on the boundary, in terms of powers of H 1 (Ω)-norms, by combining the elliptic regularity of weak solutions with Gagliardo–Nirenberg interpolation inequality.
Authors
- Maya Chhetri (ORCID: https://orcid.org/0000-0002-4822-3217)
- Nsoki Mavinga (ORCID: https://orcid.org/0000-0002-0305-6670)
- Rosa Pardo (ORCID: https://orcid.org/0000-0003-1914-9203)
Institutions
- Swarthmore College (US)
- Universidad Complutense de Madrid (ES)
- University of North Carolina at Greensboro (US)
Publication Details
- Journal
- Nonlinear Analysis
- Published
- 2026-04-20
- DOI
- https://doi.org/10.1016/j.na.2026.114127
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Simons Foundation
- Universidad Complutense de Madrid
- Ministerio de Economía y Competitividad