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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2605.12712 |
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| _version_ | 1866910213888540672 |
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| author | Maienshein, Daniel Manfredi, Juan J. |
| author_facet | Maienshein, Daniel Manfredi, Juan J. |
| contents | We first provide a classical analysis proof of a version of the Alexandroff-Bakelman-Pucci inequality (ABP) for compactly supported $C^2$ functions in dimension $2$, inspired by the symplectic geometry proof method of Viterbo, which avoids convexity or contact sets. We then show how the proof may be modified to remove the compact support hypothesis and recover the usual statement of ABP, which includes a boundary term. We also discuss the possibility (and difficulties) of extending a pure classical analysis proof to dimension $3$ and above. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12712 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Classical Analysis Counterpart of Viterbo's Symplectic Geometry Proof of ABP in the Plane Maienshein, Daniel Manfredi, Juan J. Analysis of PDEs 35J15, 35B50, 53D12 We first provide a classical analysis proof of a version of the Alexandroff-Bakelman-Pucci inequality (ABP) for compactly supported $C^2$ functions in dimension $2$, inspired by the symplectic geometry proof method of Viterbo, which avoids convexity or contact sets. We then show how the proof may be modified to remove the compact support hypothesis and recover the usual statement of ABP, which includes a boundary term. We also discuss the possibility (and difficulties) of extending a pure classical analysis proof to dimension $3$ and above. |
| title | A Classical Analysis Counterpart of Viterbo's Symplectic Geometry Proof of ABP in the Plane |
| topic | Analysis of PDEs 35J15, 35B50, 53D12 |
| url | https://arxiv.org/abs/2605.12712 |