# Functions with prescribed singularities

Giovanni Alberti; S. Baldo; G. Orlandi

Journal of the European Mathematical Society (2003)

- Volume: 005, Issue: 3, page 275-311
- ISSN: 1435-9855

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topAlberti, Giovanni, Baldo, S., and Orlandi, G.. "Functions with prescribed singularities." Journal of the European Mathematical Society 005.3 (2003): 275-311. <http://eudml.org/doc/277650>.

@article{Alberti2003,

abstract = {The distributional $k$-dimensional Jacobian of a map $u$ in the Sobolev space
$W^\{1,k−1\}$ which takes values in the sphere $S^\{k−1\}$ can be viewed as the boundary of a rectifiable current of codimension $k$ carried by (part of) the singularity of $u$ which is topologically relevant. The main purpose of this paper is to investigate the range of the
Jacobian operator; in particular, we show that any boundary $M$ of codimension $k$ can be realized as Jacobian of a Sobolev map valued in $S^\{k−1\}$. In case $M$ is polyhedral, the map we construct is smooth outside $M$ plus an additional polyhedral set of lower dimension, and
can be used in the constructive part of the proof of a $\Gamma $-convergence result for functionals of Ginzburg-Landau type, as described in [2].},

author = {Alberti, Giovanni, Baldo, S., Orlandi, G.},

journal = {Journal of the European Mathematical Society},

keywords = {Jacobian; Sobolev maps; singular maps; integral currents; rectifiability; dipole construction; complete intersections; Brouwer degree; coarea formula; Ginzburg-Landau functionals; Ginzburg-Landau functional; Jacobian; Sobolev map; integral currents; Brouwer degree; dipole construction; coarea formula},

language = {eng},

number = {3},

pages = {275-311},

publisher = {European Mathematical Society Publishing House},

title = {Functions with prescribed singularities},

url = {http://eudml.org/doc/277650},

volume = {005},

year = {2003},

}

TY - JOUR

AU - Alberti, Giovanni

AU - Baldo, S.

AU - Orlandi, G.

TI - Functions with prescribed singularities

JO - Journal of the European Mathematical Society

PY - 2003

PB - European Mathematical Society Publishing House

VL - 005

IS - 3

SP - 275

EP - 311

AB - The distributional $k$-dimensional Jacobian of a map $u$ in the Sobolev space
$W^{1,k−1}$ which takes values in the sphere $S^{k−1}$ can be viewed as the boundary of a rectifiable current of codimension $k$ carried by (part of) the singularity of $u$ which is topologically relevant. The main purpose of this paper is to investigate the range of the
Jacobian operator; in particular, we show that any boundary $M$ of codimension $k$ can be realized as Jacobian of a Sobolev map valued in $S^{k−1}$. In case $M$ is polyhedral, the map we construct is smooth outside $M$ plus an additional polyhedral set of lower dimension, and
can be used in the constructive part of the proof of a $\Gamma $-convergence result for functionals of Ginzburg-Landau type, as described in [2].

LA - eng

KW - Jacobian; Sobolev maps; singular maps; integral currents; rectifiability; dipole construction; complete intersections; Brouwer degree; coarea formula; Ginzburg-Landau functionals; Ginzburg-Landau functional; Jacobian; Sobolev map; integral currents; Brouwer degree; dipole construction; coarea formula

UR - http://eudml.org/doc/277650

ER -

## Citations in EuDML Documents

top- Ilaria Fragalà, Fenomeni di concentrazione per energie di tipo Ginzburg-Landau
- Robert L. Jerrard, Local minimizers with vortex filaments for a Gross-Pitaevsky functional
- Francesco Ghiraldin, Variational approximation of a functional of Mumford–Shah type in codimension higher than one
- Guido De Philippis, Weak notions of jacobian determinant and relaxation
- Guido De Philippis, Weak notions of Jacobian determinant and relaxation

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