Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909591813488640 |
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| author | Kim, Kyeongbae Lee, Ho-Sik Prasad, Harsh |
| author_facet | Kim, Kyeongbae Lee, Ho-Sik Prasad, Harsh |
| contents | We establish certain oscillation estimates for weak solutions to nonlinear, anomalous phase transitions modeled on the nonlocal two-phase Stefan problem. The problem is singular in time, is scaling deficient and influenced by far-off effects. We study the the problem in a geometry adapted to the solution and obtain oscillation estimates in intrinsically scaled cylinders. Furthermore, via certain uniform estimates, we construct a continuous weak solution to the corresponding initial boundary value problem with a quantitative modulus of continuity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17383 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem Kim, Kyeongbae Lee, Ho-Sik Prasad, Harsh Analysis of PDEs We establish certain oscillation estimates for weak solutions to nonlinear, anomalous phase transitions modeled on the nonlocal two-phase Stefan problem. The problem is singular in time, is scaling deficient and influenced by far-off effects. We study the the problem in a geometry adapted to the solution and obtain oscillation estimates in intrinsically scaled cylinders. Furthermore, via certain uniform estimates, we construct a continuous weak solution to the corresponding initial boundary value problem with a quantitative modulus of continuity. |
| title | Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.17383 |