Another look at qualitative properties of eigenvalues using effective Hamiltonians
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866908393809117184 |
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| author | Mazari-Fouquer, Idriss |
| author_facet | Mazari-Fouquer, Idriss |
| contents | The goal of this paper is to review several qualitative properties of well-known eigenvalue problems using a different perspective based on the theory of effective Hamiltonians, working exclusively on the Hopf-Cole transform of the equation. We revisit some monotonicity results as well as the derivation of several scaling limits by means of the Donsker-Varadhan formula, and we point out several differences between the case of quadratic Hamiltonians and non-quadratic ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08740 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Another look at qualitative properties of eigenvalues using effective Hamiltonians Mazari-Fouquer, Idriss Analysis of PDEs The goal of this paper is to review several qualitative properties of well-known eigenvalue problems using a different perspective based on the theory of effective Hamiltonians, working exclusively on the Hopf-Cole transform of the equation. We revisit some monotonicity results as well as the derivation of several scaling limits by means of the Donsker-Varadhan formula, and we point out several differences between the case of quadratic Hamiltonians and non-quadratic ones. |
| title | Another look at qualitative properties of eigenvalues using effective Hamiltonians |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.08740 |