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BY 4.0 license Open Access Published by De Gruyter Open Access October 31, 2020

A dynamical approach to the variational inequality on modified elastic graphs

  • Shinya Okabe EMAIL logo and Kensuke Yoshizawa
From the journal Geometric Flows


We consider the variational inequality on modified elastic graphs. Since the variational inequality is derived from the minimization problem for the modified elastic energy defined on graphs with the unilateral constraint, a solution to the variational inequality can be constructed by the direct method of calculus of variations. In this paper we prove the existence of solutions to the variational inequality via a dynamical approach. More precisely, we construct an L2-type gradient flow corresponding to the variational inequality and prove the existence of solutions to the variational inequality via the study on the limit of the flow.

MSC 2010: 35K25; 53C44; 35K86; 49J40


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Received: 2020-03-29
Accepted: 2020-08-31
Published Online: 2020-10-31

© 2020 Shinya Okabe et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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