Regularity results for a penalized boundary obstacle problem
In this paper we are concerned with a two-penalty boundary obstacle problem of interest in thermics, fluid dynamics and electricity. Specifically, we prove existence, uniqueness and optimal regularity of the solutions, and we establish structural properties of the free boundary. A central role is pl...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-10-01
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| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/mine.2021007/fulltext.html |
| _version_ | 1819072176222896128 |
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| author | Donatella Danielli Rohit Jain |
| author_facet | Donatella Danielli Rohit Jain |
| author_sort | Donatella Danielli |
| collection | DOAJ |
| description | In this paper we are concerned with a two-penalty boundary obstacle problem of interest in thermics, fluid dynamics and electricity. Specifically, we prove existence, uniqueness and optimal regularity of the solutions, and we establish structural properties of the free boundary. A central role is played by the monotonicity of ad hoc Almgren- and Monneau-type functionals. |
| first_indexed | 2024-12-21T17:33:34Z |
| format | Article |
| id | doaj.art-7798b4ed898e4e148cf7eb8ec33edadf |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-12-21T17:33:34Z |
| publishDate | 2021-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-7798b4ed898e4e148cf7eb8ec33edadf2022-12-21T18:55:51ZengAIMS PressMathematics in Engineering2640-35012021-10-013112310.3934/mine.2021007Regularity results for a penalized boundary obstacle problemDonatella Danielli0Rohit Jain11 Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN 47907, USA2 Materiall, 500 E Calaveras, Suite 240, Milpitas, CA 95035, USAIn this paper we are concerned with a two-penalty boundary obstacle problem of interest in thermics, fluid dynamics and electricity. Specifically, we prove existence, uniqueness and optimal regularity of the solutions, and we establish structural properties of the free boundary. A central role is played by the monotonicity of ad hoc Almgren- and Monneau-type functionals.https://www.aimspress.com/article/10.3934/mine.2021007/fulltext.htmlfree boundary problemsobstacle problemspenalized boundary conditionsmonotonicity formulassemi-permeable membranes |
| spellingShingle | Donatella Danielli Rohit Jain Regularity results for a penalized boundary obstacle problem Mathematics in Engineering free boundary problems obstacle problems penalized boundary conditions monotonicity formulas semi-permeable membranes |
| title | Regularity results for a penalized boundary obstacle problem |
| title_full | Regularity results for a penalized boundary obstacle problem |
| title_fullStr | Regularity results for a penalized boundary obstacle problem |
| title_full_unstemmed | Regularity results for a penalized boundary obstacle problem |
| title_short | Regularity results for a penalized boundary obstacle problem |
| title_sort | regularity results for a penalized boundary obstacle problem |
| topic | free boundary problems obstacle problems penalized boundary conditions monotonicity formulas semi-permeable membranes |
| url | https://www.aimspress.com/article/10.3934/mine.2021007/fulltext.html |
| work_keys_str_mv | AT donatelladanielli regularityresultsforapenalizedboundaryobstacleproblem AT rohitjain regularityresultsforapenalizedboundaryobstacleproblem |