Eremeyev, Victor A.; dell’Isola, Francesco On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains. (English) Zbl 07590432 Math. Mech. Solids 27, No. 3, 433-445 (2022). Summary: We provide the proof of an existence and uniqueness theorem for weak solutions of the equilibrium problem in linear dilatational strain gradient elasticity for bodies occupying, in the reference configuration, Lipschitz domains with edges. The considered elastic model belongs to the class of so-called incomplete strain gradient continua whose potential energy density depends quadratically on linear strains and on the gradient of dilatation only. Such a model has many applications, e.g., to describe phenomena of interest in poroelasticity or in some situations where media with scalar microstructure are necessary. We present an extension of the previous results by V. A. Eremeyev et al. [Z. Angew. Math. 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