Publication: Elliptic problems on the space of weighted with the distance to the boundary integrable functions revisited
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Department of Mathematics Texas State University
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.
Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems (2012). Electronic Journal of Differential Equations, Conference 21 (2014),
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