The paper deals with evaluation of the energy functional and its derivatives for a mixed boundary value problem of linear elasticity in a domain with a singularly perturbed boundary. An elastic body \(\Omega\) contains a crack \(\Gamma^\delta\) that includes a straight (unperturbed) section and a small extension determined by a function \(x_2= \psi(x_1)\) over a small interval \((x_1\in(0,\delta))\). The authors claim that the derivative, with respect to \(\delta\), of the energy functional “does not depend on the function \(\psi\) provided that function \(\psi\) is chosen from a quite narrow class, i.e., if this function is smooth enough”. Furthermore, the article states that “the Griffith criterion does not distinguish any possible crack propagation shapes determined by the functions \(\psi\in W^{2,0}_p(0,1)\)”. One would expect to see an analysis of singular fields in the vicinity of singularly perturbed boundary \(\Gamma^\delta\), but such analysis is absent in the present article.