L estimates for the Laplacian via blow-up
In this note we provide a new proof of the W 2 , p Calderón-Zygmund regularity estimates for the Laplacian, i.e., Δ u = f and its parabolic counterpart ∂ t u − Δ u = f . Our proof is an adaptation of a contradiction and compactness argument that so far had been only used to prove estimates in Hölder spaces. This new approach is simpler than previous ones, and avoids the use of any interpolation theorem.
Authors
- Xavier Ros‐Oton (ORCID: https://orcid.org/0000-0003-1046-168X)
- Jan Lewenstein-Sanpera
Institutions
- Institució Catalana de Recerca i Estudis Avançats (ES)
- Centre de Recerca Matemàtica (ES)
- Universitat de Barcelona (ES)
Publication Details
- Journal
- Journal of Differential Equations
- Published
- 2025-06-02
- DOI
- https://doi.org/10.1016/j.jde.2025.113478
- Citations
- 1
- Primary Topic
- Advanced Harmonic Analysis Research
- Type
- article
- Field-Weighted Citation Impact
- 3.73
Funders
- European Commission
- European Research Council
- Agència de Gestió d'Ajuts Universitaris i de Recerca
- Agencia Estatal de Investigación
- H2020 European Research Council
- HORIZON EUROPE European Research Council