A Brunn-Minkowski inequality for Schrödinger operators with Kato class potentials
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915975181369344 |
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| author | Carbotti, Alessandro |
| author_facet | Carbotti, Alessandro |
| contents | In this paper we prove a Brunn-Minkowski inequality for the first Dirichlet eigenvalue of a Schrödinger type operator $\mathcal{H}_V:=-\operatorname{div}(A\nabla)+V$, where $V$ is convex and Kato decomposable, using the trace class property of the generated semigroup. As a consequence, we obtain the log-concavity of the ground state using the ultracontractivity of the semigroup, and also the strong log-concavity under additional assumptions on $Ω$ and $V$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29989 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Brunn-Minkowski inequality for Schrödinger operators with Kato class potentials Carbotti, Alessandro Analysis of PDEs 35E10, 35J25, 35P15, 52A40 In this paper we prove a Brunn-Minkowski inequality for the first Dirichlet eigenvalue of a Schrödinger type operator $\mathcal{H}_V:=-\operatorname{div}(A\nabla)+V$, where $V$ is convex and Kato decomposable, using the trace class property of the generated semigroup. As a consequence, we obtain the log-concavity of the ground state using the ultracontractivity of the semigroup, and also the strong log-concavity under additional assumptions on $Ω$ and $V$. |
| title | A Brunn-Minkowski inequality for Schrödinger operators with Kato class potentials |
| topic | Analysis of PDEs 35E10, 35J25, 35P15, 52A40 |
| url | https://arxiv.org/abs/2603.29989 |