| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4604841 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2006 | 7 Pages |
Abstract
RésuméÀ la suite d'une question soulevée dans un travail de Brezis–Marcus–Ponce [5] on montre que si μ est une mesure de Radon diffuse et singulière sur l'ouvert U de Rd, il n'existe pas d'application linéaire continue f↦(uf,gf) de L1(μ) dans H1(U)×L1(U) telle que f⋅μ=Δuf+gf au sens de D′(U). On indique ensuite une généralisation.
Investigating a question raised in a recent paper of Brezis–Marcus–Ponce [5] we show that if μ is a singular continuous Radon measure in the open subset U of Rd, there is no continuous linear map f↦(uf,gf) from L1(μ) to H1(U)×L1(U) such that f⋅μ=Δuf+gf in the sense of distributions. A generalization is also described.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
