A nonlocal transmission problem on a hybrid continuous-discrete domain
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914393751552000 |
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| author | Abbas, Hafida Azzouz, Abdelhalim |
| author_facet | Abbas, Hafida Azzouz, Abdelhalim |
| contents | We study a quadratic nonlocal variational problem on a hybrid domain formed by a compact interval and finitely many discrete points. The associated energy splits into continuous, discrete, and interface contributions. Our main estimate shows that the interface term yields a coercive coupling between the two phases and provides an equivalent hybrid norm. As a consequence, we prove existence and uniqueness of a minimizer for the corresponding variational problem and characterize it as the unique weak solution of the associated hybrid Euler--Lagrange system. The latter combines a nonlocal integral equation on the continuous component with a finite nonlocal algebraic system on the discrete nodes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_14178 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A nonlocal transmission problem on a hybrid continuous-discrete domain Abbas, Hafida Azzouz, Abdelhalim Analysis of PDEs 26A33, 35R11, 46E35 We study a quadratic nonlocal variational problem on a hybrid domain formed by a compact interval and finitely many discrete points. The associated energy splits into continuous, discrete, and interface contributions. Our main estimate shows that the interface term yields a coercive coupling between the two phases and provides an equivalent hybrid norm. As a consequence, we prove existence and uniqueness of a minimizer for the corresponding variational problem and characterize it as the unique weak solution of the associated hybrid Euler--Lagrange system. The latter combines a nonlocal integral equation on the continuous component with a finite nonlocal algebraic system on the discrete nodes. |
| title | A nonlocal transmission problem on a hybrid continuous-discrete domain |
| topic | Analysis of PDEs 26A33, 35R11, 46E35 |
| url | https://arxiv.org/abs/2603.14178 |