TY - JOUR
T1 - Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints
AU - Arroyo-Rabasa, Adolfo
AU - De Philippis, Guido
AU - Rindler, Filip
N1 - Funding Information:
Filip Rindler acknowledges the support from an EPSRC Research Fellowship on Singularities in Nonlinear PDEs (EP/L018934/1)
Publisher Copyright:
© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.
PY - 2020/7/1
Y1 - 2020/7/1
N2 - We show general lower semicontinuity and relaxation theorems for linear-growth integral functionals defined on vector measures that satisfy linear PDE side constraints (of arbitrary order). These results generalize several known lower semicontinuity and relaxation theorems for BV, BD, and for more general first-order linear PDE side constrains. Our proofs are based on recent progress in the understanding of singularities of measure solutions to linear PDEs and of the generalized convexity notions corresponding to these PDE constraints.
AB - We show general lower semicontinuity and relaxation theorems for linear-growth integral functionals defined on vector measures that satisfy linear PDE side constraints (of arbitrary order). These results generalize several known lower semicontinuity and relaxation theorems for BV, BD, and for more general first-order linear PDE side constrains. Our proofs are based on recent progress in the understanding of singularities of measure solutions to linear PDEs and of the generalized convexity notions corresponding to these PDE constraints.
KW - Functional on measures
KW - Lower semicontinuity
UR - http://www.scopus.com/inward/record.url?scp=85040994921&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85040994921&partnerID=8YFLogxK
U2 - 10.1515/acv-2017-0003
DO - 10.1515/acv-2017-0003
M3 - Article
AN - SCOPUS:85040994921
SN - 1864-8258
VL - 13
SP - 219
EP - 255
JO - Advances in Calculus of Variations
JF - Advances in Calculus of Variations
IS - 3
ER -