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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.31018 |
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| _version_ | 1866910271893667840 |
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| author | Chen, Hua Liu, Xiaochun Wei, Yawei Zhang, Mengnan |
| author_facet | Chen, Hua Liu, Xiaochun Wei, Yawei Zhang, Mengnan |
| contents | This paper concerns a class of non-divergence nonlinear elliptic equations driven by the cone degenerate Laplacian, which is motivated by cone calculus. We establish the existence of viscosity solutions by proving the Alexandrov-Bakelman-Pucci and Hölder estimates. Furthermore, we obtain the existence of weak solutions by proving the equivalence between weak solutions and viscosity solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31018 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence results for nonlinear cone degenerate Laplace equations Chen, Hua Liu, Xiaochun Wei, Yawei Zhang, Mengnan Analysis of PDEs This paper concerns a class of non-divergence nonlinear elliptic equations driven by the cone degenerate Laplacian, which is motivated by cone calculus. We establish the existence of viscosity solutions by proving the Alexandrov-Bakelman-Pucci and Hölder estimates. Furthermore, we obtain the existence of weak solutions by proving the equivalence between weak solutions and viscosity solutions. |
| title | Existence results for nonlinear cone degenerate Laplace equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.31018 |