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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.01190 |
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| _version_ | 1866911086033240064 |
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| author | Wang, Jiangwen Yin, Yunwen Jiang, Feida |
| author_facet | Wang, Jiangwen Yin, Yunwen Jiang, Feida |
| contents | In this paper, we consider a kind of degenerate normalized $p$-Laplacian equation with general variable exponents. We establish local $C^{1,α'}$ regularity of viscosity solutions by making use of the compactness argument, scaling techniques and the localized oscillating method. In addition, we also obtain almost optimal pointwise $C^{1,τ} $ regularity for degenerate free transmission problem related to normalized $ p$-Laplacian. Our argument is based on a new improved oscillation-type estimate combined with a localized analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_01190 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Regularity of solutions to degenerate normalized $p$-Laplacian equation with general variable exponents Wang, Jiangwen Yin, Yunwen Jiang, Feida Analysis of PDEs In this paper, we consider a kind of degenerate normalized $p$-Laplacian equation with general variable exponents. We establish local $C^{1,α'}$ regularity of viscosity solutions by making use of the compactness argument, scaling techniques and the localized oscillating method. In addition, we also obtain almost optimal pointwise $C^{1,τ} $ regularity for degenerate free transmission problem related to normalized $ p$-Laplacian. Our argument is based on a new improved oscillation-type estimate combined with a localized analysis. |
| title | Regularity of solutions to degenerate normalized $p$-Laplacian equation with general variable exponents |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2303.01190 |