Elliptic problems on the space of weighted with the distance to the boundary integrable functions revisited
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 wh...
| Authors: | , |
|---|---|
| Format: | article |
| Publication Date: | 2014 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/33990 |
| Online Access: | https://hdl.handle.net/20.500.14352/33990 |
| Access Level: | Open access |
| Keyword: | 517.9 Very weak solutions semilinear elliptic equations distance to the boundary weighted spaces measure Hardy inequalities Hardy spaces Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias |
| Summary: | 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. |
|---|