The $C^{1,\alpha}$ boundary Harnack in slit domain and its application to the Signorini problem
We prove the $C^{2,\alpha}$ regularity of the free boundary in the Signorini problem with variable coefficients. We use a $C^{1,\alpha}$ boundary Harnack inequality in slit domain. The key method is to study a non-standard degenerate elliptic equation and obtain a $C^{1,\alpha}$ Schauder estimate.
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | We prove the $C^{2,\alpha}$ regularity of the free boundary in the Signorini
problem with variable coefficients. We use a $C^{1,\alpha}$ boundary Harnack
inequality in slit domain. The key method is to study a non-standard degenerate
elliptic equation and obtain a $C^{1,\alpha}$ Schauder estimate. |
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| DOI: | 10.48550/arxiv.2307.12466 |