On the fractional Schödinger equation with variable coefficients
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909376120356864 |
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| author | Kenig, C. E. Pilod, D. Ponce, G. Vega, L. |
| author_facet | Kenig, C. E. Pilod, D. Ponce, G. Vega, L. |
| contents | We study the initial value problem (IVP) associated to the semi-linear fractional Schödinger equation with variable coefficients. We deduce several properties of the anisotropic fractional elliptic operator modelling the dispersion relation and use them to establish the local well-posedness for the corresponding IVP. Also, we obtain unique continuation results concerning the solutions of this problem. These are consequences of uniqueness properties that we prove for the fractional elliptic operator with variable coefficients |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the fractional Schödinger equation with variable coefficients Kenig, C. E. Pilod, D. Ponce, G. Vega, L. Analysis of PDEs Primary: 35Q55. Secondary: 35B05 We study the initial value problem (IVP) associated to the semi-linear fractional Schödinger equation with variable coefficients. We deduce several properties of the anisotropic fractional elliptic operator modelling the dispersion relation and use them to establish the local well-posedness for the corresponding IVP. Also, we obtain unique continuation results concerning the solutions of this problem. These are consequences of uniqueness properties that we prove for the fractional elliptic operator with variable coefficients |
| title | On the fractional Schödinger equation with variable coefficients |
| topic | Analysis of PDEs Primary: 35Q55. Secondary: 35B05 |
| url | https://arxiv.org/abs/2411.01300 |