What question did this study set out to answer?

This research aims to investigate weak solutions for a coupled system of elliptic equations and their regularity properties.

April 23, 2026Open Access

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

Puntos clave

This research aims to investigate weak solutions for a coupled system of elliptic equations and their regularity properties.
Applied De Giorgi-Nash-Moser iteration scheme.
Combined elliptic regularity with Gagliardo-Nirenberg interpolation inequality.
Focused on estimating weak solutions under critical and subcritical growth.
Established that weak solutions are in L∞(Ω) under critical growth conditions.
Provided explicit L∞(Ω) estimates for weak solutions with subcritical growth.
Demonstrated the relationship between estimates and H1(Ω)-norms.

Resumen

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.

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Cite This Study

Chhetri et al. (Mon,) studied this question.

synapsesocial.com/papers/69e9b71b85696592c86eb2ba https://doi.org/https://doi.org/10.1016/j.na.2026.114127

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