Open Access
| Issue |
ESAIM: COCV
Volume 32, 2026
|
|
|---|---|---|
| Article Number | 48 | |
| Number of page(s) | 30 | |
| DOI | https://doi.org/10.1051/cocv/2026031 | |
| Published online | 15 June 2026 | |
- M. Giaquinta, G. Modica and J. Soucek, Liquid crystals: relaxed energies, dipoles, singular lines and singular points. Ann. Sc. Norm. Sup. Pisa 17 (1990) 415–437. [Google Scholar]
- M. Giaquinta, G. Modica and J. SouCek, Cartesian Currents in the Calculus of Variations. II. Variational Problems. Ergebnisse der Mathematik und ihrer Grenzgebiete, no. 38. Springer-Verlag, Berlin (1998). [Google Scholar]
- G. Angelsberg, Large solutions of biharmonic maps in four dimensions. Calc. Var. 30 (2007) 417–447. [Google Scholar]
- M.K. Cooper, Critical O(d)-equivariant biharmonic maps. Calc. Var. 54 (2015) 2895–2919. [Google Scholar]
- H. Brezis, J.M. Coron and E.H. Lieb, Harmonic maps with defects. Commun. Math. Phys. 107 (1986) 649–705. [Google Scholar]
- M. Giaquinta, G. Modica and J. Soucek, Cartesian Currents in the Calculus of Variations. I. Cartesian Currents. Ergebnisse der Mathematik und ihrer Grenzgebiete, no. 37. Springer-Verlag, Berlin (1998). [Google Scholar]
- P. Bousquet, A.C. Ponce and J. Van Schaftingen, Generic topological screening and approximation of Sobolev maps. Preprint (2025). See: https://arxiv.org/abs/2501.18149. [Google Scholar]
- M. Giaquinta and D. Mucci, Maps into manifolds and currents: area and W1'2-, W1/2-, BV -energies. Edizioni della Normale, C.R.M. Series, Sc. Norm. Sup. Pisa (2006). [Google Scholar]
- L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Math. Monographs, Oxford (2000). [Google Scholar]
- M. Silhavy, Divergence measure fields and Cauchy's stress theorem. Rend. Sem. Mat. Univ. Padova 113 (2005) 15–45. [Google Scholar]
- G.E. Comi, Refined Gauss-Green formulas and evolution problems for Radon measures. Ph.D. Thesis. Scuola Normale Superiore, Pisa (2020). Available at cvgmt.sns.it/paper/4579/. [Google Scholar]
- H. Federer and W.H. Fleming, Normal and integral currents. Ann. of Math. 72 (1960) 458–520. [Google Scholar]
- R. Schoen and K. Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps. J. Diff. Geom. 18 (1983) 253–268. [Google Scholar]
- M. Giaquinta, G. Modica and J. SouScek, Cartesian currents and variational problems for mappings into spheres. Ann. Sc. Norm. Sup. Pisa 16 (1989) 393–485. [Google Scholar]
- H. Federer, Real flat chains, cochains and variational problems. Indiana Univ. Math. J. 24 (1974) 351–407. [Google Scholar]
- F. Morgan, Area minimizing currents bounded by multiples of curves. Rend. Circ. Mat. Palermo 33 (1984) 37–46. [Google Scholar]
- B. White, The least area bounded by multiples of a curve. Proc. Am,. Math. Soc. 90 (1984) 230–232. [Google Scholar]
- F. Bethuel and X.M. Zheng, Density of smooth functions between two manifolds in Sobolev spaces. J. Funct. Anal. 80 (1988) 60–75. [Google Scholar]
- F. Bethuel, The approximation problem for Sobolev maps between manifolds. Acta Math. 167 (1992) 153–206. [Google Scholar]
- F. Bethuel, H. Brezis and J.M. Coron, Relaxed energies for harmonic maps, in Variational methods, edited by H. Berestycki, J.M. Coron and J. Ekeland. Birkauser, Basel (1990) 37–52. [Google Scholar]
- M. Giaquinta, G. Modica and J. SouScek, The Dirichlet energy of mappings with values into the sphere. Manuscr. Math. 65 (1989) 489–507. [Google Scholar]
- F.J. Almgren, W. Browder and E.H. Lieb, Co-area, liquid crystals, and minimal surfaces, in Partial Differential Equations. Springer Lecture Notes in Mathematics 1306 (1988) 1–22. [Google Scholar]
- M. Giaquinta and D. Mucci, The relaxed Dirichlet energy of mappings into a manifold. Calc. Var. 24 (2005) 155–166. [Google Scholar]
- A. Gastel and J. Nerf, Density of smooth maps in Wk,p(M, N) for a close to critical domain dimension. Ann. Glob. Anal. Geom. 39 (2011) 107–129. [Google Scholar]
- P. Bousquet, A.C. Ponce and J. Van Schaftingen, Strong density for higher order Sobolev spaces into compact manifolds. J. Eur. Math. Soc. 17 (2015) 763–817. [Google Scholar]
- M.-C. Hong and C. Wang, Regularity and relaxed problems of minimizing biharmonic maps into spheres. Calc. Var. 23 (2004) 425–450. [Google Scholar]
- F. Bethuel, A characterization of maps in H1(B3,S2) which can be approximated by smooth maps. Ann. Inst. H. Poincaré C Anal. Non Linéaire 7 (1990) 269–286. [Google Scholar]
- F. Bethuel, J.-M. Coron, F. Demengel and F. Helein, A cohomological criterion for density of smooth maps in Sobolev spaces between two manifolds, in Nematics (Orsay, 1990), 15-23, NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 332 15–23. Kluwer Acad. Publ., Dordrecht (1991). [Google Scholar]
- M. Giaquinta and D. Mucci, The BV-energy of maps into a manifold: relaxation and density results. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 5 (2006) 483–548. [Google Scholar]
- E. Acerbi and D. Mucci, Curvature-dependent energies: a geometric and analytical approach. Proc. Roy. Soc. Edinburgh, Sect. A 147A (2017) 449–503. [Google Scholar]
- E. Acerbi and D. Mucci, Curvature-dependent energies: the elastic case. Nonl. Anal. 153 (2017) 7–34. [Google Scholar]
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