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Reduced problem results in dimension n k
The lim inf inequality for the dimension-reduced problem .
Origin of the model and preliminaries
Table of contents :
Introduction
1 Ane cost function
1.1 Introduction
1.2 Preliminaries for the chapter
1.3 Local Result
1.4 Equicoercivity and -liminf
1.5 -limsup inequality
1.6 Numerical Approximation
2 Multidimensional case
2.1 Introduction
2.2 Reduced problem results in dimension n k
2.3 Compactness
2.4 -liminf inequality
2.5 -limsup inequality
3 The k-dimensional problem
3.1 Introduction
3.2 Compactness and k-rectiability
3.3 -liminf inequality
3.4 -limsup inequality
3.5 Discussion about the results
4 Piecewise ane cost functions
4.1 Introduction
4.2 Remarks
4.3 The -limit of the phase eld functional
4.3.1 The lim inf inequality for the dimension-reduced problem .
4.3.2 The lim inf inequality
4.3.3 Equicoercivity
4.3.4 The lim sup inequality
4.4 Numerical experiments
4.4.1 Discretization
4.4.2 Optimization
4.4.3 Experimental results
5 Generalized cost functions
5.1 Introduction
5.2 Origin of the model and preliminaries
5.3 Proof of Theorem 5.1
Conclusion
A Density result for vector measures in R2
B Reduced problem in dimension n k
B.1 Auxiliary problem
B.2 Study of the transition energy
B.3 Proof of Proposition 2.1
B.4 Proof of Proposition 2.2
B.5 Proof of Proposition 2.3
C Slicing of measures
D Resume substantiel en langue francaise
