Hölder Continuity and Harnack estimate for non-homogeneous parabolic equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910436209721344 |
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| author | Arya, Vedansh Julin, Vesa |
| author_facet | Arya, Vedansh Julin, Vesa |
| contents | In this paper we continue the study on intrinsic Harnack inequality for non- homogeneous parabolic equations in non-divergence form initiated by the first author in [1]. We establish a forward-in-time intrinsic Harnack inequality, which in particular implies the Hölder continuity of the solutions. We also provide a Harnack type estimate on global scale which quantifies the strong minimum principle. In the time-independent setting, this together with [1] provides an alternative proof of the generalized Harnack inequality proven by the second author in [9]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_03283 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hölder Continuity and Harnack estimate for non-homogeneous parabolic equations Arya, Vedansh Julin, Vesa Analysis of PDEs In this paper we continue the study on intrinsic Harnack inequality for non- homogeneous parabolic equations in non-divergence form initiated by the first author in [1]. We establish a forward-in-time intrinsic Harnack inequality, which in particular implies the Hölder continuity of the solutions. We also provide a Harnack type estimate on global scale which quantifies the strong minimum principle. In the time-independent setting, this together with [1] provides an alternative proof of the generalized Harnack inequality proven by the second author in [9]. |
| title | Hölder Continuity and Harnack estimate for non-homogeneous parabolic equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.03283 |