Díaz Díaz, Jesús IldefonsoRakotoson, Jean-Michel2023-06-192023-06-1920141072-6691https://hdl.handle.net/20.500.14352/33990Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems (2012). Electronic Journal of Differential Equations, Conference 21 (2014),We revisit the regularity of very weak solution to second-order elliptic equations Lu = f in Ω with u = 0 on ∂Ω for f ∈ L1 (Ω, δ), δ(x) the distance to the boundary ∂Ω. While doing this, we extend our previous results(and many others in the literature)by allowing the presence of distributions f+g which are more general than Radon measures (more precisely with g in the dual of suitable Lorentz-Sobolev spaces) and by making weaker assumptions on the coefficients of L. One of the new tools is a Hardy type inequality developed recently by the second author. Applications to the study of the gradient of solutions of some singular semilinear equations are also given.engElliptic problems on the space of weighted with the distance to the boundary integrable functions revisitedjournal articlehttp://ejde.math.txstate.edu/Volumes/2014/90/begout.pdfopen access517.9Very weak solutionssemilinear elliptic equationsdistance to the boundaryweighted spaces measureHardy inequalitiesHardy spacesEcuaciones diferenciales1202.07 Ecuaciones en Diferencias