Lower closure for orientor fields by lower semicontinuity of outer integral functionals

1985 ◽  
Vol 139 (1) ◽  
pp. 349-359 ◽  
Author(s):  
E. J. Balber
Keyword(s):  
Lower Semicontinuity ◽  
Integral Functionals ◽  
Orientor Fields ◽  
Lower Closure

scholarly journals Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints

2020 ◽  
Vol 13 (3) ◽  
pp. 219-255 ◽  
Author(s):  
Adolfo Arroyo-Rabasa ◽  
Guido De Philippis ◽  
Filip Rindler
Keyword(s):  
Lower Semicontinuity ◽  
Generalized Convexity ◽  
Linear Growth ◽  
Arbitrary Order ◽  
Integral Functionals ◽  
Vector Measures ◽  
First Order ◽  
Linear Pde ◽  
Side Constraints ◽  
Linear Pdes

AbstractWe 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.

A lower closure theorem for autonomous orientor fields

1988 ◽  
Vol 110 (3-4) ◽  
pp. 249-254 ◽  
Author(s):  
Luigi Ambrosio
Keyword(s):  
Differential Inclusion ◽  
Closure Property ◽  
Closure Theorem ◽  
Set Valued Mapping ◽  
Orientor Fields ◽  
Lower Closure ◽  
Lower Closure Theorem ◽  
Image Position

SynopsisGiven a set valued mapping ∑: ℝ → ∑n, we prove a closure property with respect to -convergence for the differential inclusionunder very mild assumptions on ∑.

A remark on the L 1 -lower semicontinuity for integral functionals in BV

2003 ◽  
Vol 112 (3) ◽  
pp. 313-323 ◽  
Author(s):  
Nicola Fusco ◽  
Flavia Giannetti ◽  
Anna Verde
Keyword(s):  
Lower Semicontinuity ◽  
Integral Functionals
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