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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2504.00452 |
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| _version_ | 1866913769363341312 |
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| author | Sato, Takuya |
| author_facet | Sato, Takuya |
| contents | We consider the free boundary problems of degenerate elliptic equations that describe the level set formulation of the interface motion evolved by anisotropic forced mean curvature flows. The type of free boundary problems in this paper was initially studied as the first-order Hamilton-Jacobi-Isaacs equations arising in pursuit-evasion differential games and applied to the models of first-order front propagation in Soravia (1994). In this paper, we consider an extension of these free boundary problems to the second-order equations and give a deterministic game representation based on a discrete approximation scheme in Kohn and Serfaty (2006). Furthermore, we prove the comparison principle for our free boundary problems by using the framework of time-discrete games. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00452 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A game approach to free boundary problems of anisotropic forced mean curvature flow equations Sato, Takuya Analysis of PDEs 35J25, 35J93, 49L25, 91A05 We consider the free boundary problems of degenerate elliptic equations that describe the level set formulation of the interface motion evolved by anisotropic forced mean curvature flows. The type of free boundary problems in this paper was initially studied as the first-order Hamilton-Jacobi-Isaacs equations arising in pursuit-evasion differential games and applied to the models of first-order front propagation in Soravia (1994). In this paper, we consider an extension of these free boundary problems to the second-order equations and give a deterministic game representation based on a discrete approximation scheme in Kohn and Serfaty (2006). Furthermore, we prove the comparison principle for our free boundary problems by using the framework of time-discrete games. |
| title | A game approach to free boundary problems of anisotropic forced mean curvature flow equations |
| topic | Analysis of PDEs 35J25, 35J93, 49L25, 91A05 |
| url | https://arxiv.org/abs/2504.00452 |