In this thesis we investigate variational problems involving 1-dimensional sets (e.g., curves, networks) and variational inequalities related to obstacle-type dynamics from a twofold prospective. On one side, we provide variational approximations and convex relaxations of the relevant energies and dynamics, moving mainly within the framework of Gamma-convergence and of convex analysis. On the other side, we thoroughly investigate the numerical optimization of the corresponding approximating energies, both to recover optimal 1-dimensional structures and to accurately simulate the actual dynamics.
| Identifer | oai:union.ndltd.org:unitn.it/oai:iris.unitn.it:11572/369106 |
| Date | January 2019 |
| Creators | Bonafini, Mauro |
| Contributors | Bonafini, Mauro |
| Publisher | Università degli studi di Trento, place:TRENTO |
| Source Sets | Università di Trento |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/closedAccess |
| Relation | firstpage:1, lastpage:97, numberofpages:97 |
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