Approximation of length minimization problems among compact connected\n sets
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Bibliographic record
Abstract
In this paper we provide an approximation \\`a la Ambrosio-Tortorelli of some\nclassical minimization problems involving the length of an unknown\none-dimensional set, with an additional connectedness constraint, in dimension\ntwo. We introduce a term of new type relying on a weighted geodesic distance\nthat forces the minimizers to be connected at the limit. We apply this approach\nto approximate the so-called Steiner Problem, but also the average distance\nproblem, and finally a problem relying on the p-compliance energy. The proof of\nconvergence of the approximating functional, which is stated in terms of\nGamma-convergence relies on technical tools from geometric measure theory, as\nfor instance a uniform lower bound for a sort of average directional Minkowski\ncontent of a family of compact connected sets.\n
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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