A Variational link between the Olech-Opial inequality, the Wirtinger inequality, and Emden-Fowler equations
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911541725495296 |
|---|---|
| author | Pain, Jean-Christophe |
| author_facet | Pain, Jean-Christophe |
| contents | We establish a structural connection between the classical Olech-Opial inequality and the Wirtinger inequality. Using an integral identity involving the mixed energy term $uu'$, we derive a nonlinear interpolation inequality linking these two results. The optimal constant is characterized by a variational problem whose extremals satisfy an Emden-Fowler equation. An explicit expression of the optimal constant is obtained in terms of the Beta function. This approach provides a natural bridge between mixed-energy integral inequalities, classical spectral estimates, and nonlinear boundary value problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23239 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Variational link between the Olech-Opial inequality, the Wirtinger inequality, and Emden-Fowler equations Pain, Jean-Christophe Analysis of PDEs Functional Analysis We establish a structural connection between the classical Olech-Opial inequality and the Wirtinger inequality. Using an integral identity involving the mixed energy term $uu'$, we derive a nonlinear interpolation inequality linking these two results. The optimal constant is characterized by a variational problem whose extremals satisfy an Emden-Fowler equation. An explicit expression of the optimal constant is obtained in terms of the Beta function. This approach provides a natural bridge between mixed-energy integral inequalities, classical spectral estimates, and nonlinear boundary value problems. |
| title | A Variational link between the Olech-Opial inequality, the Wirtinger inequality, and Emden-Fowler equations |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2603.23239 |