Abstract We address a problem that extends fundamental classical result of continuum mechanics from the time its inception, as well answers question in recent, modern nonlinear elastic theory dislocations. Interestingly, implication our latter case is qualitatively different well-established analog linear It if $$u\in C^2({\mathbb {R}}^n;{\mathbb {R}}^n)$$ <mml:math xmlns:mml="http://www.w3.org...