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Volumn 26, Issue 2, 1996, Pages 149-169

A free boundary value problem of nematic liquid crystals with variable degree of orientation

Author keywords

A free boundary value problem; Harmonic maps into a cone; Liquid crystals; Regularity theory

Indexed keywords


EID: 0041539578     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(94)00266-K     Document Type: Article
Times cited : (1)

References (18)
  • 1
    • 84990553603 scopus 로고
    • Nonlinear theory of defects in nematic liquid crystals. Phase transitions and flow phenomena
    • LIN F. H., Nonlinear theory of defects in nematic liquid crystals. Phase transitions and flow phenomena, Communs pure. appl. Math. 42, 309-334 (1988).
    • (1988) Communs Pure. Appl. Math. , vol.42 , pp. 309-334
    • Lin, F.H.1
  • 2
    • 0042093104 scopus 로고
    • Point and line singularities in liquid crystals
    • (Edited by H. BERESTYCKY, J. M. CORON and I. EKELAND). Birkhauser, Boston
    • HARDT R., Point and line singularities in liquid crystals, in Variational Methods (Edited by H. BERESTYCKY, J. M. CORON and I. EKELAND). Birkhauser, Boston (1990).
    • (1990) Variational Methods
    • Hardt, R.1
  • 3
    • 84990557427 scopus 로고
    • On nematic liquid crystals with variable degree of orientation
    • LIN F. H., On nematic liquid crystals with variable degree of orientation. Communs pure. appl. Math. 44, 453-468 (1991).
    • (1991) Communs Pure. Appl. Math. , vol.44 , pp. 453-468
    • Lin, F.H.1
  • 4
    • 0039124674 scopus 로고
    • An optimal estimate for the singular set of harmonic map in the free boundary
    • DUZAAR F. & STEFFEN K., An optimal estimate for the singular set of harmonic map in the free boundary, J. reine angew. Math. 401, 157-187 (1989).
    • (1989) J. Reine Angew. Math. , vol.401 , pp. 157-187
    • Duzaar, F.1    Steffen, K.2
  • 5
    • 84974774431 scopus 로고
    • A partial regularity thoerem for harmonic maps at a free boundary
    • DUZAAR F. & STEFFEN K., A partial regularity thoerem for harmonic maps at a free boundary, Asymptotic Analysis 2, 299-334 (1989).
    • (1989) Asymptotic Analysis , vol.2 , pp. 299-334
    • Duzaar, F.1    Steffen, K.2
  • 6
    • 84990602579 scopus 로고
    • Partially constrained boundary conditions with energy minimizing mappings
    • HARDT R. & LIN F. H., Partially constrained boundary conditions with energy minimizing mappings, Communs pure. appl. Math. 15, 309-334 (1989).
    • (1989) Communs Pure. Appl. Math. , vol.15 , pp. 309-334
    • Hardt, R.1    Lin, F.H.2
  • 7
    • 0039124669 scopus 로고
    • Harmonic mappings with partially free boundary
    • BALDES A., Harmonic mappings with partially free boundary, Manuscripta Math. 40, 225-275 (1982).
    • (1982) Manuscripta Math. , vol.40 , pp. 225-275
    • Baldes, A.1
  • 8
    • 0012944267 scopus 로고
    • Harmonic maps which solve a free boundary problem
    • GULLIVER R. & JOST J., Harmonic maps which solve a free boundary problem, J. reine angew. Math. 381, 61-89 (1987).
    • (1987) J. Reine Angew. Math. , vol.381 , pp. 61-89
    • Gulliver, R.1    Jost, J.2
  • 10
    • 51249177075 scopus 로고
    • Existence of minimal energy configulations of nematic liquid crystals with variable degree of orientation
    • AMBROSIO L., Existence of minimal energy configulations of nematic liquid crystals with variable degree of orientation, Manuscripta Math. 68, 215-228 (1990).
    • (1990) Manuscripta Math. , vol.68 , pp. 215-228
    • Ambrosio, L.1
  • 11
    • 51249177335 scopus 로고
    • Regularity of solutions of degenerate elliptic variational problem
    • AMBROSIO L., Regularity of solutions of degenerate elliptic variational problem, Manuscripta Math. 68, 309-326 (1990).
    • (1990) Manuscripta Math. , vol.68 , pp. 309-326
    • Ambrosio, L.1
  • 12
    • 0038868969 scopus 로고
    • Harmonic maps into round cones and singularities of nematic liquid crystals
    • HARDT R. & LIN F. H., Harmonic maps into round cones and singularities of nematic liquid crystals, Math. Z. 213, 575-593 (1993).
    • (1993) Math. Z. , vol.213 , pp. 575-593
    • Hardt, R.1    Lin, F.H.2
  • 13
    • 85030018522 scopus 로고    scopus 로고
    • On Ericksen's model for liquid crystals
    • to appear
    • LIN F. H. & POON C., On Ericksen's model for liquid crystals, J. Geom. Analysis (to appear)
    • J. Geom. Analysis
    • Lin, F.H.1    Poon, C.2
  • 15
    • 0000276285 scopus 로고
    • A unique continuation theorem for the exterior differential forms on Riemannian manifolds
    • ARONNSZAJN N., KRZYWICKI A. & SZARSKI J., A unique continuation theorem for the exterior differential forms on Riemannian manifolds, Ark. Math. 4, 417-453 (1962).
    • (1962) Ark. Math. , vol.4 , pp. 417-453
    • Aronnszajn, N.1    Krzywicki, A.2    Szarski, J.3
  • 16
    • 84966226124 scopus 로고
    • The singular sets of areas minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo 2 with arbitrary codimension
    • FEDERER H., The singular sets of areas minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo 2 with arbitrary codimension, Bull. Am. math. Soc. 76, 767-771 (1970).
    • (1970) Bull. Am. Math. Soc. , vol.76 , pp. 767-771
    • Federer, H.1
  • 17
    • 0005332561 scopus 로고
    • Dirichlet's problem for multiple valued functions and the regularity of mass minimizing integral currents
    • (Edited by M. OBATA), North-Holland, Amsterdam
    • ALMGREN F. J., Dirichlet's problem for multiple valued functions and the regularity of mass minimizing integral currents, in Minimal Submanifolds and Geodesics (Edited by M. OBATA), pp. 1-6. North-Holland, Amsterdam (1979).
    • (1979) Minimal Submanifolds and Geodesics , pp. 1-6
    • Almgren, F.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.