RT Journal Article
T1 Elliptic problems on the space of weighted with the distance to the boundary integrable functions revisited
A1 Díaz Díaz, Jesús Ildefonso
A1 Rakotoson, Jean-Michel
AB 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.
PB Department of Mathematics Texas State University
SN 1072-6691
YR 2014
FD 2014
LK https://hdl.handle.net/20.500.14352/33990
UL https://hdl.handle.net/20.500.14352/33990
LA eng
NO Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems (2012). Electronic Journal of Differential Equations, Conference 21 (2014),
NO Unión Europea. FP7
NO DGISPI, Spain
DS Docta Complutense
RD 6 abr 2025