Korn type inequalities for objective structures
- We establish discrete Korn type inequalities for particle systems within the general class of objective structures that represents a far reaching generalization of crystal lattice structures. For space filling configurations whose symmetry group is a general space group we obtain a full discrete Korn inequality. For systems with non-trivial codimension our results provide an intrinsic rigidity estimate within the extended dimensions of the structure. As their continuum counterparts in elasticity theory, such estimates are at the core of energy estimates and, hence, a stability analysis for a wide class of atomistic particle systems.
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| Author: | Bernd SchmidtGND, Martin Steinbach |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1253044 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/125304 |
| ISSN: | 0021-7824OPAC |
| Parent Title (French): | Journal de Mathématiques Pures et Appliquées |
| Publisher: | Elsevier BV |
| Place of publication: | Amsterdam |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2025 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2025/09/20 |
| Volume: | 204 |
| First Page: | 103779 |
| DOI: | https://doi.org/10.1016/j.matpur.2025.103779 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Nichtlineare Analysis | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand) |
