Remark on isolated removable singularities of harmonic maps in two dimensions
For a ball $B_R(0)\subset\mathbb{R}^2$, we provide sufficient conditions such that a harmonic map $u\in C^\infty(B_R(0)\setminus\{0\}, N)$, with a self-similar bound on its gradient, belong to $C^\infty(B_R(0))$. These conditions also guarantee the triviality of such harmonic maps when $R=\infty$.
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| Format: | Article |
| Language: | English |
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Texas State University
2025-08-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/85/abstr.html |
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| _version_ | 1849331445380677632 |
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| author | Changyou Wang |
| author_facet | Changyou Wang |
| author_sort | Changyou Wang |
| collection | DOAJ |
| description | For a ball $B_R(0)\subset\mathbb{R}^2$, we provide sufficient conditions such that
a harmonic map $u\in C^\infty(B_R(0)\setminus\{0\}, N)$, with a self-similar bound
on its gradient, belong to $C^\infty(B_R(0))$.
These conditions also guarantee the triviality of such harmonic maps when $R=\infty$. |
| format | Article |
| id | doaj-art-c450eebe0eb5409e805872e4b9d02b8c |
| institution | Kabale University |
| issn | 1072-6691 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj-art-c450eebe0eb5409e805872e4b9d02b8c2025-08-20T03:46:36ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912025-08-01202585,15Remark on isolated removable singularities of harmonic maps in two dimensionsChangyou Wang0 Purdue Univ., West Lafayette, IN, USA For a ball $B_R(0)\subset\mathbb{R}^2$, we provide sufficient conditions such that a harmonic map $u\in C^\infty(B_R(0)\setminus\{0\}, N)$, with a self-similar bound on its gradient, belong to $C^\infty(B_R(0))$. These conditions also guarantee the triviality of such harmonic maps when $R=\infty$.http://ejde.math.txstate.edu/Volumes/2025/85/abstr.htmlharmonic mapsremovable isolated singularity |
| spellingShingle | Changyou Wang Remark on isolated removable singularities of harmonic maps in two dimensions Electronic Journal of Differential Equations harmonic maps removable isolated singularity |
| title | Remark on isolated removable singularities of harmonic maps in two dimensions |
| title_full | Remark on isolated removable singularities of harmonic maps in two dimensions |
| title_fullStr | Remark on isolated removable singularities of harmonic maps in two dimensions |
| title_full_unstemmed | Remark on isolated removable singularities of harmonic maps in two dimensions |
| title_short | Remark on isolated removable singularities of harmonic maps in two dimensions |
| title_sort | remark on isolated removable singularities of harmonic maps in two dimensions |
| topic | harmonic maps removable isolated singularity |
| url | http://ejde.math.txstate.edu/Volumes/2025/85/abstr.html |
| work_keys_str_mv | AT changyouwang remarkonisolatedremovablesingularitiesofharmonicmapsintwodimensions |