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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Rigidity and Geometry of Microstructures
Bernd KirchheimAbstract
Existence and regularity of solutions to partial differential inclusion is investigated. A central question is whether pairwise incompatibility of the admissible gradients enforces triviality of all solutions. We obtain first finite counterexamples and exactly describe the complexity which they must have - a question partially motivated by the study of the non-convex energy landscapes of shape memory alloys.
For this purpose we develop a flexible and unifying method how to solve partial differential inclusion, a new kind of regularity results for the hyperbolic Monge-Ampere equation and a geometric approach to rank-one convexity establishing its stability properties.
- Received:
- 17.01.03
- Published:
- 17.01.03
- MSC Codes:
- 74N15, 35L70, 26B25, 35R70, 74N05, 35G30, 35F20
- Keywords:
- hyperbolic monge-ampere equation, partial differential inclusions, rank-one connection and rigidity, geometry and stability of rank-one convexity