Formation of cracks under deformations with .nite energy

Hajlasz, Piotr; Koskela, Pekka
February 2004
Calculus of Variations & Partial Differential Equations;Feb2004, Vol. 19 Issue 2, p221
Academic Journal
With a map f : O ? Rn, O ? Rn, that belongs to the John Ball class Ap,q+(O) where n - 1 < p < n and q = p/(p - 1) one can associate a set valued map F whose values F(x) ? Rn are subsets ofRn describing the topological character of the singularity of f at x ? O. �verak conjectured that Hn-1(F(S)) = 0, where S is the set of points at which f is not continuous and Hn-1 is the Hausdorff measure. The purpose of our paper is to confirm this expectation.


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