Special Session 156: Structure and dynamics of solutions for nonlinear elliptic and parabolic equations

Stability of pinned $p$-elasticae
Kensuke Yoshizawa
Nagasaki University
Japan
Co-Author(s):    Tatsuya Miura
Abstract:
Euler's elastica is a critical point of the bending energy under the fixed length constraint, and its $L^p$-counterpart is called $p$-elastica. In this talk, I will present a characterization of the stability of $p$-elasticae under the pinned boundary condition. The key ingredient is a new ``cut-and-paste'' method that does not rely on the second variation but instead exploits the geometric invariance of the functional. This talk is based on joint work with Tatsuya Miura (Kyoto University).