BV solutions constructed using the epsilon-neighborhood method^{∗, ∗∗, ∗∗∗}

Department of Mathematics, University of Stuttgart, Allmandring 5b, 70569 Stuttgart, Germany.
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Received: 13 February 2013
Revised: 17 June 2014

Abstract

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 ε and then taking the limit ε → 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)].