Regularity of the One-phase Free Boundaries
This open access book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regularity theory and is still an object of intensive res...
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| Format: | Online |
| Język: | angielski |
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Springer Nature
2023
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| Hasła przedmiotowe: | |
| Dostęp online: | ONIX_20230317_9783031132384_31 |
| Etykiety: |
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| _version_ | 1869520959864569856 |
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| author | Velichkov, Bozhidar |
| author_browse | Velichkov, Bozhidar |
| author_facet | Velichkov, Bozhidar |
| author_sort | Velichkov, Bozhidar |
| collection | Directory of Open Access Books |
| description | This open access book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regularity theory and is still an object of intensive research. The exposition is organized around four main theorems, which are dedicated to the one-phase functional in its simplest form. Many of the methods and the techniques presented here are very recent and were developed in the context of different free boundary problems. We also give the detailed proofs of several classical results, which are based on some universal ideas and are recurrent in the free boundary, PDE and the geometric regularity theories. This book is aimed at graduate students and researches and is accessible to anyone with a moderate level of knowledge of elliptical PDEs. |
| format | Online |
| id | doab-20.500.12854ir-98509 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | Springer Nature |
| publisherStr | Springer Nature |
| record_format | ojs |
| spelling | doab-20.500.12854ir-985092025-07-17T12:16:02Z Regularity of the One-phase Free Boundaries Velichkov, Bozhidar Free Boundary Problems Regularity One-phase Problem Bernoulli Free Boundary Problem Alt-Caffarelli Monotonicity Formulas Epiperimetric Inequality Partial Differential Equations thema EDItEUR::P Mathematics and Science::PB Mathematics::PBU Optimization thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis thema EDItEUR::P Mathematics and Science::PB Mathematics::PBU Optimization thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis This open access book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regularity theory and is still an object of intensive research. The exposition is organized around four main theorems, which are dedicated to the one-phase functional in its simplest form. Many of the methods and the techniques presented here are very recent and were developed in the context of different free boundary problems. We also give the detailed proofs of several classical results, which are based on some universal ideas and are recurrent in the free boundary, PDE and the geometric regularity theories. This book is aimed at graduate students and researches and is accessible to anyone with a moderate level of knowledge of elliptical PDEs. 2023-03-20T09:15:59Z 2023-03-20T09:15:59Z 2023-03-17T15:20:53Z 2023 book ONIX_20230317_9783031132384_31 https://library.oapen.org/handle/20.500.12657/61877 9783031132384 https://directory.doabooks.org/handle/20.500.12854/98509 eng Lecture Notes of the Unione Matematica Italiana open access image/jpeg image/jpeg n/a n/a https://library.oapen.org/bitstream/20.500.12657/61877/1/978-3-031-13238-4.pdf https://library.oapen.org/bitstream/20.500.12657/61877/1/978-3-031-13238-4.pdf Springer Nature Springer International Publishing 10.1007/978-3-031-13238-4 10.1007/978-3-031-13238-4 9fa3421d-f917-4153-b9ab-fc337c396b5a Horizon 2020 Framework Programme 934fa25c-7607-42a3-b320-9719e66e012e 9783031132384 Springer International Publishing 247 Cham [...] open access |
| spellingShingle | Free Boundary Problems Regularity One-phase Problem Bernoulli Free Boundary Problem Alt-Caffarelli Monotonicity Formulas Epiperimetric Inequality Partial Differential Equations thema EDItEUR::P Mathematics and Science::PB Mathematics::PBU Optimization thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis thema EDItEUR::P Mathematics and Science::PB Mathematics::PBU Optimization thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis Velichkov, Bozhidar Regularity of the One-phase Free Boundaries |
| title | Regularity of the One-phase Free Boundaries |
| title_full | Regularity of the One-phase Free Boundaries |
| title_fullStr | Regularity of the One-phase Free Boundaries |
| title_full_unstemmed | Regularity of the One-phase Free Boundaries |
| title_short | Regularity of the One-phase Free Boundaries |
| title_sort | regularity of the one phase free boundaries |
| topic | Free Boundary Problems Regularity One-phase Problem Bernoulli Free Boundary Problem Alt-Caffarelli Monotonicity Formulas Epiperimetric Inequality Partial Differential Equations thema EDItEUR::P Mathematics and Science::PB Mathematics::PBU Optimization thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis thema EDItEUR::P Mathematics and Science::PB Mathematics::PBU Optimization thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis |
| topic_facet | Free Boundary Problems Regularity One-phase Problem Bernoulli Free Boundary Problem Alt-Caffarelli Monotonicity Formulas Epiperimetric Inequality Partial Differential Equations thema EDItEUR::P Mathematics and Science::PB Mathematics::PBU Optimization thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis thema EDItEUR::P Mathematics and Science::PB Mathematics::PBU Optimization thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis |
| url | ONIX_20230317_9783031132384_31 |
| work_keys_str_mv | AT velichkovbozhidar regularityoftheonephasefreeboundaries |