BV solutions constructed using the epsilon-neighborhood method

Minh, Mach Nguyet

ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 1, pp. 188-207.

We study a certain class of weak solutions to rate-independent systems, which is constructed by using the local minimality in a small neighborhood of order $\epsilon$ and then taking the limit $\epsilon \to 0$. We show that the resulting solution satisfies both the weak local stability and the new energy-dissipation balance, similarly to the BV solutions constructed by vanishing viscosity introduced recently by Mielke et al. [A. Mielke, R. Rossi and G. Savaré, Discrete Contin. Dyn. Syst. 2 (2010) 585–615; ESAIM: COCV 18 (2012) 36–80; To appear in J. Eur. Math. Soc. (2016)].

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