Some Remarks on Pohozaev-Type Identities
In this note we present some Pohozaev-type identities that have been recently established in a joint work with Paul Laurain and Tristan Rivière in the framework of half-harmonic maps defined either on the real line or on the unit circle with values into a closed n-dimensional manifold. Weak half-har...
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| Format: | Article |
| Language: | English |
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University of Bologna
2018-12-01
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| Series: | Bruno Pini Mathematical Analysis Seminar |
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| Online Access: | https://mathematicalanalysis.unibo.it/article/view/8963 |
| _version_ | 1818977972516814848 |
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| author | Francesca Da Lio |
| author_facet | Francesca Da Lio |
| author_sort | Francesca Da Lio |
| collection | DOAJ |
| description | In this note we present some Pohozaev-type identities that have been recently established in a joint work with Paul Laurain and Tristan Rivière in the framework of half-harmonic maps defined either on the real line or on the unit circle with values into a closed n-dimensional manifold. Weak half-harmonic maps are defined as critical points of the so-called half Dirichlet energy.By using the invariance of the half Dirichlet energy with respect to the trace of the Möbius transformations we derive a countable family of relations involving the Fourier coefficients of weak half-harmonic maps. We also present a short overview of Pohozaev formulas in 2-D in connection with Noether's theorem. |
| first_indexed | 2024-12-20T16:36:14Z |
| format | Article |
| id | doaj.art-bce04d1a0aa444ad87862d690d9228e9 |
| institution | Directory Open Access Journal |
| issn | 2240-2829 |
| language | English |
| last_indexed | 2024-12-20T16:36:14Z |
| publishDate | 2018-12-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Bruno Pini Mathematical Analysis Seminar |
| spelling | doaj.art-bce04d1a0aa444ad87862d690d9228e92022-12-21T19:33:09ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292018-12-019111513610.6092/issn.2240-2829/89637798Some Remarks on Pohozaev-Type IdentitiesFrancesca Da Lio0ETH ZürichIn this note we present some Pohozaev-type identities that have been recently established in a joint work with Paul Laurain and Tristan Rivière in the framework of half-harmonic maps defined either on the real line or on the unit circle with values into a closed n-dimensional manifold. Weak half-harmonic maps are defined as critical points of the so-called half Dirichlet energy.By using the invariance of the half Dirichlet energy with respect to the trace of the Möbius transformations we derive a countable family of relations involving the Fourier coefficients of weak half-harmonic maps. We also present a short overview of Pohozaev formulas in 2-D in connection with Noether's theorem.https://mathematicalanalysis.unibo.it/article/view/8963fractional harmonic mapsharmonic mapsmöbius transformationspohozaev formulasfourier coefficents |
| spellingShingle | Francesca Da Lio Some Remarks on Pohozaev-Type Identities Bruno Pini Mathematical Analysis Seminar fractional harmonic maps harmonic maps möbius transformations pohozaev formulas fourier coefficents |
| title | Some Remarks on Pohozaev-Type Identities |
| title_full | Some Remarks on Pohozaev-Type Identities |
| title_fullStr | Some Remarks on Pohozaev-Type Identities |
| title_full_unstemmed | Some Remarks on Pohozaev-Type Identities |
| title_short | Some Remarks on Pohozaev-Type Identities |
| title_sort | some remarks on pohozaev type identities |
| topic | fractional harmonic maps harmonic maps möbius transformations pohozaev formulas fourier coefficents |
| url | https://mathematicalanalysis.unibo.it/article/view/8963 |
| work_keys_str_mv | AT francescadalio someremarksonpohozaevtypeidentities |