Carleman factorization of layer potentials on smooth domains
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929293792116736 |
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| author | Ando, Kazunori Kang, Hyeonbae Miyanishi, Yoshihisa Putinar, Mihai |
| author_facet | Ando, Kazunori Kang, Hyeonbae Miyanishi, Yoshihisa Putinar, Mihai |
| contents | One of the unexplored benefits of studying layer potentials on smooth, closed hypersurfaces of Euclidean space is the factorization of the Neumann-Poincaré operator into a product of two self-adjoint transforms. Resurrecting some pertinent indications of Carleman and M. G. Krein, we exploit this grossly overlooked structure by confining the spectral analysis of the Neumann-Poincaré operator to the amenable $L^2$-space setting, rather than bouncing back and forth the computations between Sobolev spaces of negative or positive fractional order. An enhanced, fresh new look at symmetrizable linear transforms enters into the picture in the company of geometric-microlocal analysis techniques. The outcome is manyfold, complementing recent advances on the theory of layer potentials, in the smooth boundary setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19033 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Carleman factorization of layer potentials on smooth domains Ando, Kazunori Kang, Hyeonbae Miyanishi, Yoshihisa Putinar, Mihai Analysis of PDEs Mathematical Physics Functional Analysis 31B10 (primary), 35P20, 35J25, 47A45 (secondary) One of the unexplored benefits of studying layer potentials on smooth, closed hypersurfaces of Euclidean space is the factorization of the Neumann-Poincaré operator into a product of two self-adjoint transforms. Resurrecting some pertinent indications of Carleman and M. G. Krein, we exploit this grossly overlooked structure by confining the spectral analysis of the Neumann-Poincaré operator to the amenable $L^2$-space setting, rather than bouncing back and forth the computations between Sobolev spaces of negative or positive fractional order. An enhanced, fresh new look at symmetrizable linear transforms enters into the picture in the company of geometric-microlocal analysis techniques. The outcome is manyfold, complementing recent advances on the theory of layer potentials, in the smooth boundary setting. |
| title | Carleman factorization of layer potentials on smooth domains |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis 31B10 (primary), 35P20, 35J25, 47A45 (secondary) |
| url | https://arxiv.org/abs/2403.19033 |