Regularity and explicit L^∞ estimates for a class of nonlinear elliptic systems

2025/04/16 by Maya Chhetri, Chhetri, Maya, Nsoki Mavinga +3
Mathematics · #Nonlinear Partial Differential Equations #Navier-Stokes equation solutions #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2504.12434

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^∞(Ω). Moreover, we provide an explicit L^∞(Ω)- estimate of weak solutions with subcritical growth on the boundary, in terms of powers of H¹(Ω)-norms, by combining the elliptic regularity of weak solutions with Gagliardo--Nirenberg interpolation inequality.

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