On the Harnack inequality for time-fractional and more general non-local in time subdiffusion equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911222821027840 |
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| author | Ryszewska, Katarzyna Zacher, Rico |
| author_facet | Ryszewska, Katarzyna Zacher, Rico |
| contents | In this paper we establish the Harnack inequality for globally positive local solutions to a general class of nonlocal in time subdiffusion equations in one space dimension, which includes time-fractional diffusion equations with time order less than one. It is already known that for these equations the classical Harnack inequality does not hold if the space dimension is greater than or equal to two. Here, we complete the analysis, by providing a positive result in one space dimension. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_17992 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Harnack inequality for time-fractional and more general non-local in time subdiffusion equations Ryszewska, Katarzyna Zacher, Rico Analysis of PDEs 35R09, 45K05 In this paper we establish the Harnack inequality for globally positive local solutions to a general class of nonlocal in time subdiffusion equations in one space dimension, which includes time-fractional diffusion equations with time order less than one. It is already known that for these equations the classical Harnack inequality does not hold if the space dimension is greater than or equal to two. Here, we complete the analysis, by providing a positive result in one space dimension. |
| title | On the Harnack inequality for time-fractional and more general non-local in time subdiffusion equations |
| topic | Analysis of PDEs 35R09, 45K05 |
| url | https://arxiv.org/abs/2510.17992 |