Study demonstrates the existence of weak solutions in a nonlinear elliptic problem, suggesting uniqueness under smooth boundary conditions.
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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Choudhuri et al. (2026) studied this question.
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