Distances between homotopy classes of Ws,p(𝕊N;𝕊N)

Brezis, Haïm; Mironescu, Petru; Shafrir, Itai

doi:10.1051/cocv/2016037

Distances between homotopy classes of W^s,p(𝕊^N;𝕊^N)

Brezis, Haïm ^1,² ; Mironescu, Petru ³ ; Shafrir, Itai ²

¹ Department of Mathematics, Rutgers University, New Brunswick, NJ, USA.
² Department of Mathematics, Technion – I.I.T., 32000 Haifa, Israel.
³ Université de Lyon, Université Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 69622 Villeurbanne, France.

ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1204-1235.

Reçu le : 2016-06-06
Accepté le : 2016-06-07

Zbl

DOI : 10.1051/cocv/2016037

Classification : 46E40
Mots-clés : Sobolev spaces, degree, sphere-valued maps, homotopy classes

Affiliations des auteurs :

Brezis, Haïm ^{1, 2} ; Mironescu, Petru ³ ; Shafrir, Itai ²

@article{COCV_2016__22_4_1204_0,
     author = {Brezis, Ha{\"\i}m and Mironescu, Petru and Shafrir, Itai},
     title = {Distances between homotopy classes of {W\protect\textsuperscript{s,p}(\ensuremath{\mathbb{S}}\protect\textsuperscript{N};\ensuremath{\mathbb{S}}\protect\textsuperscript{N})}},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1204--1235},
     publisher = {EDP-Sciences},
     volume = {22},
     number = {4},
     year = {2016},
     doi = {10.1051/cocv/2016037},
     zbl = {1371.46027},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/cocv/2016037/}
}

TY  - JOUR
AU  - Brezis, Haïm
AU  - Mironescu, Petru
AU  - Shafrir, Itai
TI  - Distances between homotopy classes of Ws,p(𝕊N;𝕊N)
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2016
SP  - 1204
EP  - 1235
VL  - 22
IS  - 4
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/cocv/2016037/
DO  - 10.1051/cocv/2016037
LA  - en
ID  - COCV_2016__22_4_1204_0
ER  -

%0 Journal Article
%A Brezis, Haïm
%A Mironescu, Petru
%A Shafrir, Itai
%T Distances between homotopy classes of Ws,p(𝕊N;𝕊N)
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2016
%P 1204-1235
%V 22
%N 4
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/cocv/2016037/
%R 10.1051/cocv/2016037
%G en
%F COCV_2016__22_4_1204_0

Brezis, Haïm; Mironescu, Petru; Shafrir, Itai. Distances between homotopy classes of W^s,p(𝕊^N;𝕊^N). ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1204-1235. doi : 10.1051/cocv/2016037. http://archive.numdam.org/articles/10.1051/cocv/2016037/

Bibliographie
Cité par

L.V. Berlyand, P. Mironescu, V. Rybalko and E. Sandier, Minimax critical points in Ginzburg-Landau problems with semi-stiff boundary conditions: existence and bubbling. Commun. Partial Differential Equations 39 (2014) 946–1005. | DOI | Zbl

J. Bourgain, H. Brezis and P. Mironescu, Lifting in Sobolev spaces. J. Anal. Math. 80 (2000) 37–86. | DOI | Zbl

J. Bourgain, H. Brezis and P. Mironescu, Lifting, degree, and the distributional Jacobian revisited. Commun. Pure Appl. Math. 58 (2005) 529–551. | DOI | Zbl

J. Bourgain, H. Brezis and P. Mironescu, Complements to the paper Lifting, degree, and the distributional Jacobian revisited (2005) . | HAL

A. Boutet De Monvel-Berthier, V. Georgescu and R. Purice, A boundary value problem related to the Ginzburg–Landau model. Commun. Math. Phys. 142 (1991) 1–23. | DOI | Zbl

H. Brezis, Large harmonic maps in two dimensions, in Proc. of Symp. on Nonlinear variational problems, Isola d’Elba, 1983. Pitman, Boston, MA (1985) 33–46. | Zbl

H. Brezis, Metastable harmonic maps, in Metastability and incompletely posed problems, Minneapolis, 1985. Vol. 3 of IMA Vol. Math. Appl. Springer, New York (1987) 33–42. | Zbl

H. Brezis, New questions related to the topological degree, The unity of mathematics. In Vol. 244 of Progr. Math. Birkhäuser Boston, Boston, MA (2006) 137–154. | Zbl

H. Brezis and J.-M. Coron, Large solutions for harmonic maps in two dimensions. Commun. Math. Phys. 92 (1983) 203–215. | DOI | Zbl

H. Brezis and P. Mironescu, Sobolev maps with values into the circle. Birkhäuser. In preparation (2016).

H. Brezis and L. Nirenberg, Degree theory and BMO. I. Compact manifolds without boundaries. Selecta Math. (N.S.) 1 (1995) 197–263. | DOI | Zbl

H. Brezis, P. Mironescu and A. Ponce, $W^{1, 1}$ -maps with values into 𝕊¹, in Geometric analysis of PDE and several complex variables. Vol. 368 of Contemp. Math. Amer. Math. Soc. Providence, RI (2005) 69–100. | Zbl

H. Brezis, P. Mironescu and I. Shafrir, Distances between classes in $W^{1, 1} (Ω; 𝕊^{1})$ . In preparation (2016).

S. Levi and I. Shafrir, On the distance between homotopy classes of maps between spheres. J. Fixed Point Theory Appl. 15 (2014) 501–518. | DOI | Zbl

J. Rubinstein and I. Shafrir, The distance between homotopy classes of 𝕊¹-valued maps in multiply connected domains. Israel J. Math. 160 (2007) 41–59. | DOI | Zbl

R. Schoen and K. Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps. J. Differ. Geom. 18 (1983) 253–268. | DOI | Zbl

Cité par Sources :