Variational problems for Sobolev maps with bounded total variation that take values into the one-dimensional projective space are studied. We focus on the different features from the case of Sobolev maps with bounded conformal p-energy that take values into the p-dimensional projective space, for p ≥ 2 integer, recently studied in [19].
@article{CML_2010__2_2_181_0,
author = {Mucci, Domenico},
title = {Sobolev maps into the projective line with bounded total variation},
journal = {Confluentes Mathematici},
pages = {181--216},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {2},
number = {2},
year = {2010},
doi = {10.1142/S179374421000017X},
language = {en},
url = {http://www.numdam.org/articles/10.1142/S179374421000017X/}
}
TY - JOUR AU - Mucci, Domenico TI - Sobolev maps into the projective line with bounded total variation JO - Confluentes Mathematici PY - 2010 SP - 181 EP - 216 VL - 2 IS - 2 PB - World Scientific Publishing Co Pte Ltd UR - http://www.numdam.org/articles/10.1142/S179374421000017X/ DO - 10.1142/S179374421000017X LA - en ID - CML_2010__2_2_181_0 ER -
%0 Journal Article %A Mucci, Domenico %T Sobolev maps into the projective line with bounded total variation %J Confluentes Mathematici %D 2010 %P 181-216 %V 2 %N 2 %I World Scientific Publishing Co Pte Ltd %U http://www.numdam.org/articles/10.1142/S179374421000017X/ %R 10.1142/S179374421000017X %G en %F CML_2010__2_2_181_0
Mucci, Domenico. Sobolev maps into the projective line with bounded total variation. Confluentes Mathematici, Tome 2 (2010) no. 2, pp. 181-216. doi : 10.1142/S179374421000017X. http://www.numdam.org/articles/10.1142/S179374421000017X/
[1] E. Acerbi and G. Dal Maso, Calc. Var. Partial Diff. Eqns. 2, 329 (1994), DOI: 10.1007/BF01235534.
[2] F. J. Almgren, W. Browder and E. H. Lieb, Partial Differential Equations, Springer Lecture Notes in Math. 1306 (Springer, 1988) pp. 1–22.
[3] L. Ambrosio , N. Fusco and D. Pallara , Functions of Bounded Variation and Free Discontinuity Problems ( Oxford Univ. Press , 2000 ) .
[4] F. Bethuel, Acta Math. 167, 153 (1992), DOI: 10.1007/BF02392449.
[5] F. Bethuel and D. Chiron, Perspectives in Nonlinear Partial Differential Equations, Contemp. Math. 446 (Amer. Math. Soc., 2007) pp. 125–152.
[6] H. Brezis, J. M. Coron and E. H. Lieb, Comm. Math. Phys. 107, 649 (1986), DOI: 10.1007/BF01205490.
[7] H. Brezis, P. Mironescu and A. Ponce, Geometric Analysis of PDE and Several Complex Variables, Contemp. Math. 368 (Amer. Math. Soc., 2005) pp. 69–100.
[8] H. Federer , Geometric Measure Theory , Grundlehren math. Wissen. 153 ( Springer , 1969 ) .
[9] H. Federer and W. H. Fleming, Ann. Math. 72, 458 (1960), DOI: 10.2307/1970227.
[10] M. Giaquinta, G. Modica and J. Souček, Ann. Sc. Norm. Sup. Pisa Cl. Sci. (4) 17, 415 (1990).
[11] M. Giaquinta, G. Modica and J. Souček, Progress in Partial Differential Equations: Calculus of Variations, Applications, Pitman Research Notes in Math. Ser. 267, eds. C. Bandleet al. (Longman, 1992) pp. 27–47.
[12] M. Giaquinta, G. Modica and J. Souček, Calc. Var. Partial Diff. Eqns. 1, 87 (1993), DOI: 10.1007/BF02163266.
[13] M. Giaquinta , G. Modica and J. Souček , Cartesian Currents in the Calculus of Variations, I, II , Ergebnisse Math. Grenzgebiete (III Ser) 37 and 38 ( Springer , 1998 ) .
[14] M. Giaquinta, G. Modica and J. Souček, Selecta Math. (N. S.) 10, 359 (2004).
[15] M. Giaquinta and D. Mucci , Maps into Manifolds and Currents: Area and W1,2-, W1/2-, BV-Energies ( Edizioni della Normale , 2006 ) .
[16] R. Hardt and J. Pitts, Geometric Measure Theory and the Calculus of Variations, eds. W. K. Allard and F. J. Almgren (Amer. Math. Soc., 1996) pp. 255–295.
[17] R. Ignat, Ann. Inst. Henri Poincaré. Anal. Non Linéaire 22, 283 (2005), DOI: 10.1016/j.anihpc.2004.07.003.
[18] D. Mucci, Forum Math. 20, 859 (2008), DOI: 10.1515/FORUM.2008.041.
[19] D. Mucci, Maps into projective spaces: Liquid crystal and conformal energies, preprint 2010, at: http://cvgmt.sns.it/people/mucci/ .
[20] R. Schoen and K. Uhlenbeck, J. Diff. Geom. 18, 253 (1983).
[21] L. Simon , Lectures on Geometric Measure Theory , Proc. of the Centre for Math. Analysis 3 ( Australian National University , 1983 ) .
[22] E. H. Spanier , Algebraic Topology ( McGraw-Hill , 1986 ) .
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