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Daily Overview |
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Pms1: Partial Differential Equations with multiple scales Location: G309 Session Chair: Matthias Röger Session Chair: Ben Schweizer | |
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Lower energy scaling bounds of singular perturbation models for higher order laminates via Fourier-based localization methods Rheinische Friedrich-Wilhelms-Universität Bonn, Germany Fourier-based localization methods can be used to obtain lower scaling bounds for singular perturbation models. To illustrate this approach, we begin with a three-well problem within the theory of geometrically linearized elasticity. We then consider settings with more wells and discuss the singular perturbed Tartar square, revisiting the results by Rüland and Tribuzio (2022). We also briefly compare the technique with the results by Chan and Conti (2015), which rely on real-space localization methods, and discuss the extent to which the Fourier-based approach can be applied in the geometrically nonlinear case. The talk is based on joint works with Angkana Rüland, Antonio Tribuzio, and Timo Hofmann. | |
