A remark on elastic graphs with the symmetric cone obstacle

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Abstract

This paper is concerned with the variational problem for the elastic energy defined on symmetric graphs under the unilateral constraint. Assuming that the obstacle function satisfies the symmetric cone condition, we prove (i) uniqueness of minimizers and (ii) loss of regularity of minimizers and give (iii) complete classification of existence and nonexistence of minimizers in terms of the size of obstacle. As an application, we characterize the solution of obstacle problem as equilibrium of the corresponding dynamical problem.

Original languageEnglish
Pages (from-to)1857-1885
Number of pages29
JournalSIAM Journal on Mathematical Analysis
Volume53
Issue number2
DOIs
Publication statusPublished - 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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