Harnack inequality for anisotropic fully nonlinear equations with nonstandard growth
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917394595708928 |
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| author | Byun, Sun-Sig Kim, Hongsoo |
| author_facet | Byun, Sun-Sig Kim, Hongsoo |
| contents | We establish Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear anisotropic elliptic equations exhibiting non-standard growth conditions. A primary example of such operators is the degenerate anisotropic $(p_i)$-Laplacian. Our approach relies on the sliding paraboloid method, adapted with suitably chosen anisotropic functions to derive the basic measure estimates. A central contribution of this work is the development of a doubling property, achieved through the explicit construction of a novel barrier function. By combining these tools with the intrinsic geometry techniques introduced in [DGV08, VV25], we prove the intrinsic Harnack inequality for this class of operators under appropriate conditions on the exponents $(p_i)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07783 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Harnack inequality for anisotropic fully nonlinear equations with nonstandard growth Byun, Sun-Sig Kim, Hongsoo Analysis of PDEs 35B65, 35D40, 35J15, 35J70 We establish Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear anisotropic elliptic equations exhibiting non-standard growth conditions. A primary example of such operators is the degenerate anisotropic $(p_i)$-Laplacian. Our approach relies on the sliding paraboloid method, adapted with suitably chosen anisotropic functions to derive the basic measure estimates. A central contribution of this work is the development of a doubling property, achieved through the explicit construction of a novel barrier function. By combining these tools with the intrinsic geometry techniques introduced in [DGV08, VV25], we prove the intrinsic Harnack inequality for this class of operators under appropriate conditions on the exponents $(p_i)$. |
| title | Harnack inequality for anisotropic fully nonlinear equations with nonstandard growth |
| topic | Analysis of PDEs 35B65, 35D40, 35J15, 35J70 |
| url | https://arxiv.org/abs/2604.07783 |