The Pohozaev identity for the Spectral Fractional Laplacian
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918300163768320 |
|---|---|
| author | Barrios-Cubas, Itahisa Bonforte, Matteo González, María del Mar Torres-Latorre, Clara |
| author_facet | Barrios-Cubas, Itahisa Bonforte, Matteo González, María del Mar Torres-Latorre, Clara |
| contents | In this paper, we prove a Pohozaev identity for the Spectral Fractional Laplacian (SFL). This identity allows us to establish non-existence results for the semilinear Dirichlet problem $(-Δ|_Ω)^su = f(u)$ in star-shaped domains. The first such identity for non-local operators was established by Ros-Oton and Serra in 2014 for the Restricted Fractional Laplacian (RFL). However, the SFL differs fundamentally from the RFL, and the integration by parts strategy of Ros-Oton and Serra cannot be applied. Instead, we develop a novel spectral approach that exploits the underlying quadratic structure. Our main result expresses the identity as a Schur product of the classical Pohozaev quadratic form and a transition matrix that depends on the eigenvalues of the Laplacian and the fractional exponent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16185 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Pohozaev identity for the Spectral Fractional Laplacian Barrios-Cubas, Itahisa Bonforte, Matteo González, María del Mar Torres-Latorre, Clara Analysis of PDEs 35J61, 35R11 In this paper, we prove a Pohozaev identity for the Spectral Fractional Laplacian (SFL). This identity allows us to establish non-existence results for the semilinear Dirichlet problem $(-Δ|_Ω)^su = f(u)$ in star-shaped domains. The first such identity for non-local operators was established by Ros-Oton and Serra in 2014 for the Restricted Fractional Laplacian (RFL). However, the SFL differs fundamentally from the RFL, and the integration by parts strategy of Ros-Oton and Serra cannot be applied. Instead, we develop a novel spectral approach that exploits the underlying quadratic structure. Our main result expresses the identity as a Schur product of the classical Pohozaev quadratic form and a transition matrix that depends on the eigenvalues of the Laplacian and the fractional exponent. |
| title | The Pohozaev identity for the Spectral Fractional Laplacian |
| topic | Analysis of PDEs 35J61, 35R11 |
| url | https://arxiv.org/abs/2601.16185 |