What question did this study set out to answer?

May 2, 2026Open Access

Neumann problem with a discontinuous nonlinearity

Puntos clave

The aim is to prove the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary conditions.
Focused on a nonlinear elliptic problem driven by a discontinuous power nonlinearity.
Derived estimates to establish well-posedness of the problem.
Showed uniqueness when boundary conditions are smooth.
Proved the existence of weak solutions for the given nonlinear elliptic problem.
Established an estimate demonstrating well-posedness, implying the uniqueness of the solution for smooth boundary terms.

Resumen

This study is devoted to proving the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary data. The problem is driven by a discontinuous power nonlinearity and a nonsmooth prescribed data. Additionally, we aim to derive an estimate that proves the well-posedness of the problem. This estimate serves as an evidence for the uniqueness of the existing solution when the boundary term is “smooth”.

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