Relaxation of signed integral functionals in BV

By Jan Kristensen, Filip Rindler. 2009

104 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/97d0079c8cad7f3600f3c3f16a68d7e1420a76ff

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In Biomedical Engineering

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Characterization of Sobolev and BV Spaces (2011, background): “There has been some work involving arguments specific to particular problems, for example, time-dependent problems [53], as well as the desire to consider f that are not necessarily 1-homogeneous ([55], [56]).”
The structure of optimal parameters for image restoration problems (2015, background): “With regard to more advanced strict convergence results, we point the reader to [25,38,36].”
On the structure of A-free measures and applications (2016, background): “Besides its theoretical interest, the rank-one theorem has many applications in the theory of functions of bounded variation; we just mention the following: lower-semicontinuity and relaxation [9], [18], [26], integral representation theorems [12], Young measure theory [25], [38], [24], approximatio”
Characterization of Generalized Gradient Young Measures Generated by Sequences in W1,1 and BV (2010, methodology): “For the proof of the necessity case of the above theorem, we employ a recent lower semicontinuity result for integral functionals in BV, proved by the authors [KR08].”
Localization of nonlocal gradients in various topologies (2015, methodology): “Moreover, when using the quantity on the right hand side, Bourgain, Brezis and Mironescu [5] had shown that in the limit one recovers a constant multiple of the Lp-norm of ∇u, while we recover the exact Lp-norm of ∇u by using the left hand side.”
On the Dirichlet problem for variational integrals in BV (2012, background): “8 ([5], [6], [54])—an extension to quasiconvex integrands f is possible.”