Very weak solutions of Poisson's equation with singular data under Neumann boundary conditions (Q2017816)

The authors are concerned with the study of very weak solutions \(u\in L^1(\Omega)\) for the Poisson's equation \(-\Delta u=f\) in \(\Omega\), subject to Neumann boundary conditions. Here \(\Omega\) is a smooth and bounded domain and \(f\) is a singular data. The authors are first concerned with general existence and uniqueness results. Next, the regularity of solutions is discussed.