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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.21078 |
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| _version_ | 1866913629377396736 |
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| author | Maienshein, Daniel |
| author_facet | Maienshein, Daniel |
| contents | In the theory of viscosity solutions for second-order, degenerate elliptic PDEs, the Ishii-Lions method is a commonly used strategy, and the theorem of sums is the main analytical tool. As noted by Porretta and Priola, uniformly elliptic PDEs admit a version of the theorem of sums without the squared term due to a compactness argument. Here, we introduce a larger class of PDEs for which the compactness argument holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_21078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Compactness Condition for the Theorem of Sums in a Class of Non-Uniformly Elliptic PDEs Maienshein, Daniel Analysis of PDEs 35G20 In the theory of viscosity solutions for second-order, degenerate elliptic PDEs, the Ishii-Lions method is a commonly used strategy, and the theorem of sums is the main analytical tool. As noted by Porretta and Priola, uniformly elliptic PDEs admit a version of the theorem of sums without the squared term due to a compactness argument. Here, we introduce a larger class of PDEs for which the compactness argument holds. |
| title | A Compactness Condition for the Theorem of Sums in a Class of Non-Uniformly Elliptic PDEs |
| topic | Analysis of PDEs 35G20 |
| url | https://arxiv.org/abs/2412.21078 |