Hölder regularity for nonlocal double phase equations
We prove some regularity estimates for viscosity solutions to a class of possible degenerate and singular integro-differential equations whose leading operator switches between two different types of fractional elliptic phases, according to the zero set of a modulating coefficient . The model case i...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2019
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| _version_ | 1797055569543036928 |
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| author | De Filippis, C Palatucci, G |
| author_facet | De Filippis, C Palatucci, G |
| author_sort | De Filippis, C |
| collection | OXFORD |
| description | We prove some regularity estimates for viscosity solutions to a class of possible degenerate and singular integro-differential equations whose leading operator switches between two different types of fractional elliptic phases, according to the zero set of a modulating coefficient . The model case is driven by the following nonlocal double phase operator,
where and . Our results do also apply for inhomogeneous equations, for very general classes of measurable kernels. By simply assuming the boundedness of the modulating coefficient, we are able to prove that the solutions are Hölder continuous, whereas similar sharp results for the classical local case do require a to be Hölder continuous. To our knowledge, this is the first (regularity) result for nonlocal double phase problems. |
| first_indexed | 2024-03-06T19:12:01Z |
| format | Journal article |
| id | oxford-uuid:17190050-57dc-4985-837b-ce2c3ce0c113 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:12:01Z |
| publishDate | 2019 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:17190050-57dc-4985-837b-ce2c3ce0c1132022-03-26T10:35:06ZHölder regularity for nonlocal double phase equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:17190050-57dc-4985-837b-ce2c3ce0c113EnglishSymplectic Elements at OxfordElsevier2019De Filippis, CPalatucci, GWe prove some regularity estimates for viscosity solutions to a class of possible degenerate and singular integro-differential equations whose leading operator switches between two different types of fractional elliptic phases, according to the zero set of a modulating coefficient . The model case is driven by the following nonlocal double phase operator, where and . Our results do also apply for inhomogeneous equations, for very general classes of measurable kernels. By simply assuming the boundedness of the modulating coefficient, we are able to prove that the solutions are Hölder continuous, whereas similar sharp results for the classical local case do require a to be Hölder continuous. To our knowledge, this is the first (regularity) result for nonlocal double phase problems. |
| spellingShingle | De Filippis, C Palatucci, G Hölder regularity for nonlocal double phase equations |
| title | Hölder regularity for nonlocal double phase equations |
| title_full | Hölder regularity for nonlocal double phase equations |
| title_fullStr | Hölder regularity for nonlocal double phase equations |
| title_full_unstemmed | Hölder regularity for nonlocal double phase equations |
| title_short | Hölder regularity for nonlocal double phase equations |
| title_sort | holder regularity for nonlocal double phase equations |
| work_keys_str_mv | AT defilippisc holderregularityfornonlocaldoublephaseequations AT palatuccig holderregularityfornonlocaldoublephaseequations |