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Elliptic problems on the space of weighted with the distance to the boundary integrable functions revisited

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Díaz Díaz, Jesús Ildefonso and Rakotoson, Jean-Michel (2014) Elliptic problems on the space of weighted with the distance to the boundary integrable functions revisited. Electronic Journal of Differential Equations, Conference, 21 . pp. 45-59. ISSN 1072-6691

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Official URL: http://ejde.math.txstate.edu/Volumes/2014/90/begout.pdf



Abstract

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.


Item Type:Article
Additional Information:

Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems (2012). Electronic Journal of Differential Equations, Conference 21 (2014),

Uncontrolled Keywords:Very weak solutions; semilinear elliptic equations; distance to the boundary; weighted spaces measure; Hardy inequalities; Hardy spaces
Subjects:Sciences > Mathematics > Differential equations
ID Code:29595
Deposited On:16 Apr 2015 08:56
Last Modified:12 Dec 2018 15:06

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