On Some Transformations Associated to a Certain Cone
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917154888089600 |
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| author | Vasilyev, Vladimir Tokarev, Denis |
| author_facet | Vasilyev, Vladimir Tokarev, Denis |
| contents | A model elliptic pseudo-differential equation in $4$-faced cone is studied in Sobolev--Slobodetskii space. The Bochner kernel for such a cone is evaluated and explicit formula for unique solution to the considered equation is presented under certain restrictions on the symbol. Boundary value problem with additional integral condition is considered and unique solvability to the boundary value problem is proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16840 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Some Transformations Associated to a Certain Cone Vasilyev, Vladimir Tokarev, Denis Analysis of PDEs Functional Analysis 35J30, 47G30 A model elliptic pseudo-differential equation in $4$-faced cone is studied in Sobolev--Slobodetskii space. The Bochner kernel for such a cone is evaluated and explicit formula for unique solution to the considered equation is presented under certain restrictions on the symbol. Boundary value problem with additional integral condition is considered and unique solvability to the boundary value problem is proved. |
| title | On Some Transformations Associated to a Certain Cone |
| topic | Analysis of PDEs Functional Analysis 35J30, 47G30 |
| url | https://arxiv.org/abs/2512.16840 |