Some perspectives on (non)local phase transitions and minimal surfaces
We present here some classical and modern results about phase transitions and minimal surfaces, which are quite intertwined topics. We start from scratch, revisiting the theory of phase transitions as put forth by Lev Landau. Then, we relate the short-range phase transitions to the classical minimal...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2023-04-01
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| Series: | Bulletin of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.worldscientific.com/doi/10.1142/S1664360723300013 |
| _version_ | 1797838008339136512 |
|---|---|
| author | Serena Dipierro Enrico Valdinoci |
| author_facet | Serena Dipierro Enrico Valdinoci |
| author_sort | Serena Dipierro |
| collection | DOAJ |
| description | We present here some classical and modern results about phase transitions and minimal surfaces, which are quite intertwined topics. We start from scratch, revisiting the theory of phase transitions as put forth by Lev Landau. Then, we relate the short-range phase transitions to the classical minimal surfaces, whose basic regularity theory is presented, also in connection with a celebrated conjecture by Ennio De Giorgi. With this, we explore the recently developed subject of long-range phase transitions and relate its genuinely nonlocal regime to the analysis of fractional minimal surfaces. |
| first_indexed | 2024-04-09T15:33:51Z |
| format | Article |
| id | doaj.art-e4d05608d2b24b26aa4d73062efda7fa |
| institution | Directory Open Access Journal |
| issn | 1664-3607 1664-3615 |
| language | English |
| last_indexed | 2024-04-09T15:33:51Z |
| publishDate | 2023-04-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | Bulletin of Mathematical Sciences |
| spelling | doaj.art-e4d05608d2b24b26aa4d73062efda7fa2023-04-28T04:34:54ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152023-04-01130110.1142/S1664360723300013Some perspectives on (non)local phase transitions and minimal surfacesSerena Dipierro0Enrico Valdinoci1Department of Mathematics and Statistics, University of Western Australia, 35 Stirling, Highway, WA 6009 Crawley, AustraliaDepartment of Mathematics and Statistics, University of Western Australia, 35 Stirling, Highway, WA 6009 Crawley, AustraliaWe present here some classical and modern results about phase transitions and minimal surfaces, which are quite intertwined topics. We start from scratch, revisiting the theory of phase transitions as put forth by Lev Landau. Then, we relate the short-range phase transitions to the classical minimal surfaces, whose basic regularity theory is presented, also in connection with a celebrated conjecture by Ennio De Giorgi. With this, we explore the recently developed subject of long-range phase transitions and relate its genuinely nonlocal regime to the analysis of fractional minimal surfaces.https://www.worldscientific.com/doi/10.1142/S1664360723300013Phase transitionminimal surfacesregularity theory |
| spellingShingle | Serena Dipierro Enrico Valdinoci Some perspectives on (non)local phase transitions and minimal surfaces Bulletin of Mathematical Sciences Phase transition minimal surfaces regularity theory |
| title | Some perspectives on (non)local phase transitions and minimal surfaces |
| title_full | Some perspectives on (non)local phase transitions and minimal surfaces |
| title_fullStr | Some perspectives on (non)local phase transitions and minimal surfaces |
| title_full_unstemmed | Some perspectives on (non)local phase transitions and minimal surfaces |
| title_short | Some perspectives on (non)local phase transitions and minimal surfaces |
| title_sort | some perspectives on non local phase transitions and minimal surfaces |
| topic | Phase transition minimal surfaces regularity theory |
| url | https://www.worldscientific.com/doi/10.1142/S1664360723300013 |
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