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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.17106 |
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| _version_ | 1866914035079839744 |
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| author | Liu, Qing Manfredi, Juan J. Zhou, Xiaodan |
| author_facet | Liu, Qing Manfredi, Juan J. Zhou, Xiaodan |
| contents | We establish a superposition principle in disjoint variables for the inhomogeneous infinity-Laplace equation. We show that the sum of viscosity solutions of the inhomogeneous infinity-Laplace equation in separate domains is a viscosity solution in the product domain. This result has been used in the literature with certain particular choices of solutions to simplify regularity analysis for a general inhomogeneous infinity-Laplace equation by reducing it to the case without sign-changing inhomogeneous terms and vanishing gradient singularities. We present a proof of this superposition principle for general viscosity solutions. We also explore generalization in metric spaces using cone comparison techniques and study related properties for general elliptic and convex equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17106 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Superposition Property in Disjoint Variables for the Infinity Laplace Equation Liu, Qing Manfredi, Juan J. Zhou, Xiaodan Analysis of PDEs 35D40, 35J92 We establish a superposition principle in disjoint variables for the inhomogeneous infinity-Laplace equation. We show that the sum of viscosity solutions of the inhomogeneous infinity-Laplace equation in separate domains is a viscosity solution in the product domain. This result has been used in the literature with certain particular choices of solutions to simplify regularity analysis for a general inhomogeneous infinity-Laplace equation by reducing it to the case without sign-changing inhomogeneous terms and vanishing gradient singularities. We present a proof of this superposition principle for general viscosity solutions. We also explore generalization in metric spaces using cone comparison techniques and study related properties for general elliptic and convex equations. |
| title | Superposition Property in Disjoint Variables for the Infinity Laplace Equation |
| topic | Analysis of PDEs 35D40, 35J92 |
| url | https://arxiv.org/abs/2508.17106 |