Journal
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume 37, Issue 1-2, Pages 29-62Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-009-0250-5
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Funding
- Oxford Centre for Nonlinear Partial Differential Equations (OxPDE)
- Engineering and Physical Sciences Research Council [EP/E035027/1] Funding Source: researchfish
- EPSRC [EP/E035027/1] Funding Source: UKRI
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For integral functionals initially defined for u is an element of W-1,W-1(Omega; R-m) by integral(Omega) f(del u) dx we establish strict continuity and relaxation results in BV(Omega; R-m). The results cover the case of signed continuous integrands f : R-mxd -> R of linear growth at infinity. In particular, it is not excluded that the integrands are unbounded below.
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