Bounds on the trace mapping of LD-fields

Abstract

Bounds on the trace mappings defined on the Sobolev space W 1 1 ( Ω ) and the space L D ( 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.