메뉴 건너뛰기




Volumn 4, Issue 1, 2011, Pages 149-190

Three-term commutator estimates and the regularity of 1/2-harmonic maps into spheres

Author keywords

Commutator estimates; Harmonic map; Nonlinear elliptic PDE; Regularity of solutions

Indexed keywords


EID: 80655140871     PISSN: 21575045     EISSN: 1948206X     Source Type: Journal    
DOI: 10.2140/apde.2011.4.149     Document Type: Article
Times cited : (124)

References (20)
  • 1
    • 84876720817 scopus 로고
    • A note on Riesz potentials
    • MR 56 #16361 Zbl 0336.46038
    • D. R. Adams, "A note on Riesz potentials", Duke Mathematical J. 42:4 (1975), 765-778. MR 56 #16361 Zbl 0336.46038
    • (1975) Duke Mathematical J. , vol.42 , Issue.4 , pp. 765-778
    • Adams, D.R.1
  • 2
    • 0000278701 scopus 로고
    • Factorization theorems for Hardy spaces in several variables
    • MR 54 #843 Zbl 0326.32011
    • R. R. Coifman, R. Rochberg, and G. Weiss, "Factorization theorems for Hardy spaces in several variables", Ann. of Math. .2/ 103:3 (1976), 611-635. MR 54 #843 Zbl 0326.32011
    • (1976) Ann. of Math. .2/ , vol.103 , Issue.3 , pp. 611-635
    • Coifman, R.R.1    Rochberg, R.2    Weiss, G.3
  • 3
    • 0000021349 scopus 로고
    • Compensated compactness and Hardy spaces
    • MR 95d:46033 Zbl 0864.42009
    • R. Coifman, P.-L. Lions, Y. Meyer, and S. Semmes, "Compensated compactness and Hardy spaces", J. Math. Pures Appl. .9/ 72:3 (1993), 247-286. MR 95d:46033 Zbl 0864.42009
    • (1993) J. Math. Pures Appl. .9/ , vol.72 , Issue.3 , pp. 247-286
    • Coifman, R.1    Lions, P.-L.2    Meyer, Y.3    Semmes, S.4
  • 4
    • 0003846834 scopus 로고
    • Multiple integrals in the calculus of variations and nonlinear elliptic systems
    • Annals of Math. Studies 105, Princeton Univ. Press, . MR 86b:49003 Zbl 0516.49003
    • M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Math. Studies 105, Princeton Univ. Press, 1983. MR 86b:49003 Zbl 0516.49003
    • (1983)
    • Giaquinta, M.1
  • 5
    • 77952837586 scopus 로고    scopus 로고
    • Modern Fourier analysis
    • 2nd ed., Graduate Texts in Mathematics 250, Springer, New York, . MR 2463316 Zbl 1158.42001
    • L. Grafakos, Modern Fourier analysis, 2nd ed., Graduate Texts in Mathematics 250, Springer, New York, 2009. MR 2463316 Zbl 1158.42001
    • (2009)
    • Grafakos, L.1
  • 6
    • 84878696057 scopus 로고    scopus 로고
    • Harmonic maps
    • conservation laws and moving frames, 2nd ed., Cambridge Tracts in Mathematics 150, Cambridge University Press, Cambridge, . MR 2003g:58024 Zbl 1010.58010
    • F. Hélein, Harmonic maps, conservation laws and moving frames, 2nd ed., Cambridge Tracts in Mathematics 150, Cambridge University Press, Cambridge, 2002. MR 2003g:58024 Zbl 1010.58010
    • (2002)
    • Hélein, F.1
  • 7
    • 0012549640 scopus 로고
    • Some regularity results for quasilinear elliptic systems of second order
    • MR 51 #13446 Zbl 0317.35040
    • S. Hildebrandt and K.-O. Widman, "Some regularity results for quasilinear elliptic systems of second order", Math. Z. 142 (1975), 67-86. MR 51 #13446 Zbl 0317.35040
    • (1975) Math. Z. , vol.142 , pp. 67-86
    • Hildebrandt, S.1    Widman, K.-O.2
  • 8
    • 84878714968 scopus 로고    scopus 로고
    • Analysis of solutions to critical non-local Schrödinger equation and applications
    • F. D. Lio and T. Riviere, "Analysis of solutions to critical non-local Schrödinger equation and applications", 2010.
    • (2010)
    • Lio, F.D.1    Riviere, T.2
  • 9
    • 0003575867 scopus 로고
    • Non-homogeneous boundary value problems and applications
    • I, Grundlehren der Math. Wiss. 181, Springer, New York, . MR 50 #2670 Zbl 0223.35039
    • J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications, I, Grundlehren der Math. Wiss. 181, Springer, New York, 1972. MR 50 #2670 Zbl 0223.35039
    • (1972)
    • Lions, J.-L.1    Magenes, E.2
  • 10
    • 0004154258 scopus 로고
    • Multiple integrals in the calculus of variations
    • Grundlehren der Math. Wiss. 130, Springer, New York, . MR 34 #2380 Zbl 0142.38701
    • C. B. Morrey, Multiple integrals in the calculus of variations, Grundlehren der Math. Wiss. 130, Springer, New York, 1966. MR 34 #2380 Zbl 0142.38701
    • (1966)
    • Morrey, C.B.1
  • 11
    • 33847320537 scopus 로고    scopus 로고
    • Conservation laws for conformally invariant variational problems
    • MR 2008d:58010 Zbl 1128.58010
    • T. Rivière, "Conservation laws for conformally invariant variational problems", Invent. Math. 168:1 (2007), 1-22. MR 2008d:58010 Zbl 1128.58010
    • (2007) Invent. Math. , vol.168 , Issue.1 , pp. 1-22
    • Rivière, T.1
  • 12
    • 84878742006 scopus 로고    scopus 로고
    • The role of integrability by compensation in conformal geometric analysis
    • Available at. To appear in Analytic aspects of problems from riemannian geometry, Soc. Math. de France.
    • T. Rivière, "The role of integrability by compensation in conformal geometric analysis", 2008, Available at http://www.math.ethz.ch/~riviere/papers/integrabcomp.pdf. To appear in Analytic aspects of problems from riemannian geometry, Soc. Math. de France.
    • (2008)
    • Rivière, T.1
  • 13
    • 0003419898 scopus 로고    scopus 로고
    • Sobolev spaces of fractional order
    • Nemytskij operators, and nonlinear partial differential equations, Series in Nonlinear Analysis and Applications 3, de Gruyter., Berlin, . MR 98a:47071 Zbl 0873.35001
    • T. Runst and W. Sickel, Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations, Series in Nonlinear Analysis and Applications 3, de Gruyter., Berlin, 1996. MR 98a:47071 Zbl 0873.35001
    • (1996)
    • Runst, T.1    Sickel, W.2
  • 14
    • 84990623256 scopus 로고
    • Weak solutions and development of singularities of the SU(2) -model
    • MR 89f:58044 Zbl 0686.35081
    • J. Shatah, "Weak solutions and development of singularities of the SU(2) -model", Comm. Pure Appl. Math. 41:4 (1988), 459-469. MR 89f:58044 Zbl 0686.35081
    • (1988) Comm. Pure Appl. Math. , vol.41 , Issue.4 , pp. 459-469
    • Shatah, J.1
  • 15
    • 0000035649 scopus 로고
    • Hölder inequalities and sharp embeddings in function spaces of Bs pq and Fs p q type
    • MR 96h:46042
    • W. Sickel and H. Triebel, "Hölder inequalities and sharp embeddings in function spaces of Bs pq and Fs p q type", Z. Anal. Anwendungen 14:1 (1995), 105-140. MR 96h:46042
    • (1995) Z. Anal. Anwendungen , vol.14 , Issue.1 , pp. 105-140
    • Sickel, W.1    Triebel, H.2
  • 16
    • 0003799686 scopus 로고
    • Singular integrals and differentiability properties of functions
    • Princeton Math. Series 30, Princeton Univ. Press, . MR 44 #7280 Zbl 0207.13501
    • E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Math. Series 30, Princeton Univ. Press, 1970. MR 44 #7280 Zbl 0207.13501
    • (1970)
    • Stein, E.M.1
  • 17
    • 2142788928 scopus 로고    scopus 로고
    • An introduction to Sobolev spaces and interpolation spaces
    • Lecture Notes of the Unione Matematica Italiana 3, Springer, Berlin, and UMI, Bologna, . MR 2008g:46055 Zbl 1126.46001
    • L. Tartar, An introduction to Sobolev spaces and interpolation spaces, Lecture Notes of the Unione Matematica Italiana 3, Springer, Berlin, and UMI, Bologna, 2007. MR 2008g:46055 Zbl 1126.46001
    • (2007)
    • Tartar, L.1
  • 18
    • 0003434854 scopus 로고
    • Pseudodifferential operators and nonlinear PDE
    • Progress in Mathematics 100, Birkhäuser, Boston, . MR 92j:35193 Zbl 0746.35062
    • M. E. Taylor, Pseudodifferential operators and nonlinear PDE, Progress in Mathematics 100, Birkhäuser, Boston, 1991. MR 92j:35193 Zbl 0746.35062
    • (1991)
    • Taylor, M.E.1
  • 19
    • 0004058897 scopus 로고
    • Theory of function spaces
    • Monographs in Mathematics 78, Birkhäuser, Basel, . MR 86j:46026 Zbl 0546.46027
    • H. Triebel, Theory of function spaces, Monographs in Mathematics 78, Birkhäuser, Basel, 1983. MR 86j:46026 Zbl 0546.46027
    • (1983)
    • Triebel, H.1
  • 20
    • 0001585852 scopus 로고
    • An existence theorem for surfaces of constant mean curvature
    • MR 39 #4788 Zbl 0181.11501
    • H. C. Wente, "An existence theorem for surfaces of constant mean curvature", J. Math. Anal. Appl. 26 (1969), 318-344. MR 39 #4788 Zbl 0181.11501
    • (1969) J. Math. Anal. Appl. , vol.26 , pp. 318-344
    • Wente, H.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.