FUNCTIONS OF BOUNDED VARIATION AND FREE DISCONTINUITY PROBLEMS (Oxford Mathematical Monographs)

By Ronald F. Gariepy. 2001

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Localization of nonlocal gradients in various topologies (2015, methodology): “Before we state the theorem for the BV case, let us recall the following lemma, a fact about Radon measures possessing weak derivatives that are also Radon measures (see [2][Exercise 3.”
Heat semigroup and functions of bounded variation on Riemannian manifolds (2007, methodology): “We refer to [18] for more information on Sobolev spaces on manifolds, and to [1] for a discussion of BV in the Euclidean setting.”
Partial Regularity for BV Minimizers (2018, methodology): “x ∈ ∂Bt and by the trace theorem (see [8] Th.”
Traces of functions of bounded deformation (2013, methodology): “In the footsteps of these works, a systematic study of this space has been investigated, starting from basic properties (traces, imbeddings, Poincaré-Korn inequalities) in [3, 19, 23], to fine properties (structure of the strain measure, one-dimensional sections, approximate differentiability) in [1”