Bounds on the trace mapping of LD-fields

Bounds on the trace mappings defined on the Sobolev space W11(Ω) and the space LD(Ω)LD(Ω) of integrable strains are obtained. In the mechanics of continuous media, such bounds correspond to stress concentration—the ratio between the maximal stress in a body and the maximum of the traction applied to its boundary. The analysis leading to the bounds may be described in the mechanical context of stress theory and stress concentration.