Regularity and explicit $L^\infty$ estimates for a class of nonlinear elliptic systems

Maya Chhetri; Nsoki Mavinga; Rosa Pardo

Regularity and explicit $L^\infty$ estimates for a class of nonlinear elliptic systems

Analysis of PDEs 2025-04-18 v1

Authors: Maya Chhetri , Nsoki Mavinga , Rosa Pardo

Abstract

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 $L^\infty(\Omega)$ . Moreover, we provide an explicit $L^\infty(\Omega)$ - estimate of weak solutions with subcritical growth on the boundary, in terms of powers of $H^1(\Omega)$ -norms, by combining the elliptic regularity of weak solutions with Gagliardo--Nirenberg interpolation inequality.

Keywords

regularity for elliptic equations regularity of solutions elliptic partial differential equations

Cite

@article{arxiv.2504.12434,
  title  = {Regularity and explicit $L^\infty$ estimates for a class of nonlinear elliptic systems},
  author = {Maya Chhetri and Nsoki Mavinga and Rosa Pardo},
  journal= {arXiv preprint arXiv:2504.12434},
  year   = {2025}
}

Comments

21 pages, 3 figures

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