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oai:docta.ucm.es:20.500.14352/339902023-08-28T08:19:56Zcom_20.500.14352_14col_20.500.14352_15

Díaz Díaz, Jesús Ildefonso Rakotoson, Jean-Michel 2023-06-19T13:32:55Z 2023-06-19T13:32:55Z 2014 1072-6691 https://hdl.handle.net/20.500.14352/33990 http://ejde.math.txstate.edu/Volumes/2014/90/begout.pdf 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. eng open access Elliptic problems on the space of weighted with the distance to the boundary integrable functions revisited journal article