A singular perturbation approach to a higher-order free boundary problem

This talk addresses a higher-order variational problem with an obstacle constraint, which models thin elastic bodies adhering to non-flat solid substrates. Focusing on a one-dimensional periodic setting, we consider how physical parameters in the model affect the shapes of least energy solutions. Our main concern is the regime of small bending rigidity. To this end we first establish a Gamma-convergence result with an appropriate compactness property and then obtain a stronger convergence of least energy solutions beyond fundamental consequences of the Gamma-convergence.