Remark to dynamic constant problems for bodies with a singular memory (Q2713591)

This small article can be considered as an appendix to a paper of the author, published in [Boll. Unione Mat. Ital. VII Ser., A 9, No. 3, 581-592 (1995; Zbl 0855.73068)]. In that paper the author proves the existence of a weak solution to a nonlinear dynamic boundary contact problem for a body with singular memory and rigid obstacle. In the reviewed paper, the author relaxes one of the assumptions, namely the relation between the dimension and the ``penalty parameter'' \(\alpha \) so that the result is independent of the dimension. The problem is again solved by penalizing the contact condition. Interpolating properly, the author obtains fractional derivative estimates for an approximating sequence, which finally leads to strong convergence inside the nonlinear term. Under natural assumptions the author thus obtains the existence of a weak solution \(u\) such that \(u\in H^{1+\alpha /2,1}(\Omega)\) and \(u_t \in H^{\alpha /2,\alpha /(2-\alpha)}(\Omega)\).