Properties of the free boundary near the fixed boundary of the double obstacle problems
In this paper, we study the tangential touch and [Formula: see text] regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator. The main idea to have the properties is regarding the upper obstacle as a solution of the single obs...
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| Format: | Article |
| Language: | English |
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World Scientific Publishing
2022-12-01
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| Series: | Bulletin of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.worldscientific.com/doi/10.1142/S1664360721500090 |
| _version_ | 1811179163947630592 |
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| author | Jinwan Park |
| author_facet | Jinwan Park |
| author_sort | Jinwan Park |
| collection | DOAJ |
| description | In this paper, we study the tangential touch and [Formula: see text] regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator. The main idea to have the properties is regarding the upper obstacle as a solution of the single obstacle problem. Then, in the classification of global solutions of the double problem, it is enough to consider only two cases for the upper obstacle, a 2xn2ora 2xn2 + bx nx1for some b ∈ ℝ,b≠0. The second one is a new type of upper obstacle, which does not exist in the study of local regularity of the free boundary of the double problem. Thus, in this paper, a new type of difficulties that come from the second type upper obstacle is mainly studied. |
| first_indexed | 2024-04-11T06:31:14Z |
| format | Article |
| id | doaj.art-03b00a2f581e46bfb13d8de1acee0fe1 |
| institution | Directory Open Access Journal |
| issn | 1664-3607 1664-3615 |
| language | English |
| last_indexed | 2024-04-11T06:31:14Z |
| publishDate | 2022-12-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | Bulletin of Mathematical Sciences |
| spelling | doaj.art-03b00a2f581e46bfb13d8de1acee0fe12022-12-22T04:40:03ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152022-12-01120310.1142/S1664360721500090Properties of the free boundary near the fixed boundary of the double obstacle problemsJinwan Park0Research Institute of Mathematics, Seoul National University, Seoul 08826, KoreaIn this paper, we study the tangential touch and [Formula: see text] regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator. The main idea to have the properties is regarding the upper obstacle as a solution of the single obstacle problem. Then, in the classification of global solutions of the double problem, it is enough to consider only two cases for the upper obstacle, a 2xn2ora 2xn2 + bx nx1for some b ∈ ℝ,b≠0. The second one is a new type of upper obstacle, which does not exist in the study of local regularity of the free boundary of the double problem. Thus, in this paper, a new type of difficulties that come from the second type upper obstacle is mainly studied.https://www.worldscientific.com/doi/10.1142/S1664360721500090Free boundary problemobstacle problemdouble obstacle problemregularity of free boundary |
| spellingShingle | Jinwan Park Properties of the free boundary near the fixed boundary of the double obstacle problems Bulletin of Mathematical Sciences Free boundary problem obstacle problem double obstacle problem regularity of free boundary |
| title | Properties of the free boundary near the fixed boundary of the double obstacle problems |
| title_full | Properties of the free boundary near the fixed boundary of the double obstacle problems |
| title_fullStr | Properties of the free boundary near the fixed boundary of the double obstacle problems |
| title_full_unstemmed | Properties of the free boundary near the fixed boundary of the double obstacle problems |
| title_short | Properties of the free boundary near the fixed boundary of the double obstacle problems |
| title_sort | properties of the free boundary near the fixed boundary of the double obstacle problems |
| topic | Free boundary problem obstacle problem double obstacle problem regularity of free boundary |
| url | https://www.worldscientific.com/doi/10.1142/S1664360721500090 |
| work_keys_str_mv | AT jinwanpark propertiesofthefreeboundarynearthefixedboundaryofthedoubleobstacleproblems |