$L^p$ estimates for the Laplacian via blow-up
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908380858155008 |
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| author | Lewenstein-Sanpera, Jan Ros-Oton, Xavier |
| author_facet | Lewenstein-Sanpera, Jan Ros-Oton, Xavier |
| contents | In this note we provide a new proof of the $W^{2,p}$ Calderón-Zygmund regularity estimates for the Laplacian, i.e., $Δu=f$ and its parabolic counterpart $\partial_t u-Δu=f$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05882 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L^p$ estimates for the Laplacian via blow-up Lewenstein-Sanpera, Jan Ros-Oton, Xavier Analysis of PDEs 35B65, 35J05, 35K05 In this note we provide a new proof of the $W^{2,p}$ Calderón-Zygmund regularity estimates for the Laplacian, i.e., $Δu=f$ and its parabolic counterpart $\partial_t u-Δu=f$. 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. |
| title | $L^p$ estimates for the Laplacian via blow-up |
| topic | Analysis of PDEs 35B65, 35J05, 35K05 |
| url | https://arxiv.org/abs/2407.05882 |