On a $Γ$-limit of Willmore functionals with additional curvature penalization term

Heiner Olbermann

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arXiv · 1807.10701

On a $Γ$-limit of Willmore functionals with additional curvature penalization term

Heiner Olbermann

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Abstract

We consider the Willmore functional on graphs, with an additional penalization of the area where the curvature is non-zero. Interpreting the penalization parameter as a Lagrange multiplier, this corresponds to the Willmore functional with a constraint on the area where the graph is flat. Sending the penalization parameter to $\infty$ and rescaling suitably, we derive the limit functional in the sense of $Γ$-convergence.

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Heiner Olbermann. 2019-01-13. On a $Γ$-limit of Willmore functionals with additional curvature penalization term. https://arxiv.org/abs/1807.10701

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