메뉴 건너뛰기




Volumn 142, Issue 1, 2007, Pages 1733-1748

The monotonicity condition and a priori estimates of the Hölder norm for a class of nondiagonal elliptic systems with quadratic nonlinearity

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33846970913     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/s10958-007-0084-7     Document Type: Article
Times cited : (2)

References (32)
  • 3
    • 33846944492 scopus 로고    scopus 로고
    • English transl. of the 1st ed.: Academic Press, New York, 1968.
    • English transl. of the 1st ed.: Academic Press, New York, 1968.
  • 4
    • 0011549124 scopus 로고
    • Ein optimaler Regulariẗatssatz f̈ur schwache Lösungen gewisser elliptischer Systeme
    • M. Wiegner, "Ein optimaler Regulariẗatssatz f̈ur schwache Lösungen gewisser elliptischer Systeme," Math. Z. 147 (1976), 21-28.
    • (1976) Math. Z , vol.147 , pp. 21-28
    • Wiegner, M.1
  • 5
    • 0011663530 scopus 로고
    • On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order
    • S. Hildebrandt and K.-O. Widman, "On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order," Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 4 (1977), no. 1, 145-178.
    • (1977) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.4 , Issue.1 , pp. 145-178
    • Hildebrandt, S.1    Widman, K.-O.2
  • 6
    • 84972544463 scopus 로고
    • A regularity theory for harmonic maps
    • R. Schoen and K. Uhlenbeck, "A regularity theory for harmonic maps," J. Diff. Geom. 17 (1982), 307-335.
    • (1982) J. Diff. Geom , vol.17 , pp. 307-335
    • Schoen, R.1    Uhlenbeck, K.2
  • 7
    • 84972503995 scopus 로고
    • On the evolution of harmonic maps in higher dimensions
    • M. Struwe, "On the evolution of harmonic maps in higher dimensions," J. Diff. Geom. 28 (1988), 485-502.
    • (1988) J. Diff. Geom , vol.28 , pp. 485-502
    • Struwe, M.1
  • 8
    • 0000892935 scopus 로고
    • Régularité des applications faiblement harmoniques entre une surface et une variété riemannienne
    • F. Hélein, "Régularité des applications faiblement harmoniques entre une surface et une variété riemannienne," C. R. Acad. Sci. Paris, Sér. I, Math. 312 (1991), 591-596.
    • (1991) C. R. Acad. Sci. Paris, Sér. I, Math , vol.312 , pp. 591-596
    • Hélein, F.1
  • 9
    • 0002104157 scopus 로고
    • Partial regularity for stationary harmonic maps into spheres
    • L. C. Evans, "Partial regularity for stationary harmonic maps into spheres," Arch. Rational Mech. Anal. 116 (1991), 101-113.
    • (1991) Arch. Rational Mech. Anal , vol.116 , pp. 101-113
    • Evans, L.C.1
  • 10
    • 0000629651 scopus 로고
    • Partial regularity for harmonic maps of evolution into spheres
    • M. Feldman, "Partial regularity for harmonic maps of evolution into spheres," Commun. Partial Different. Eq. 19 (1994), 761-790.
    • (1994) Commun. Partial Different. Eq , vol.19 , pp. 761-790
    • Feldman, M.1
  • 11
    • 0038271821 scopus 로고    scopus 로고
    • Regularity for the approximated harmonic map equation and application to the heat flow for harmonic maps
    • R. Moser, "Regularity for the approximated harmonic map equation and application to the heat flow for harmonic maps," Math. Z. 243 (2003), 263-289.
    • (2003) Math. Z , vol.243 , pp. 263-289
    • Moser, R.1
  • 12
    • 18144417390 scopus 로고
    • On two-dimensional quasilinear elliptic systems
    • J. Frehse, "On two-dimensional quasilinear elliptic systems," Manuscripta Math. 28 (1979), 21-50.
    • (1979) Manuscripta Math , vol.28 , pp. 21-50
    • Frehse, J.1
  • 13
    • 29144438368 scopus 로고    scopus 로고
    • Solvability problem for nondiagonal elliptic systems with a quadratic nonlinearity in the gradient (the two-dimensional case) [in Russian]
    • A. Arkhipova, "Solvability problem for nondiagonal elliptic systems with a quadratic nonlinearity in the gradient (the two-dimensional case)" [in Russian], Zap. Nauchn. Semin. POMI 295 (2003), 5-17;
    • (2003) Zap. Nauchn. Semin. POMI , vol.295 , pp. 5-17
    • Arkhipova, A.1
  • 15
    • 33846985448 scopus 로고    scopus 로고
    • On the smoothness of weak solutions of strong-nonlinear nondiagonal elliptic systems (the two-dimensional case)
    • in Russian
    • A. Arkhipova, "On the smoothness of weak solutions of strong-nonlinear nondiagonal elliptic systems (the two-dimensional case)," Zap. Nauchn. Semin. POMI [in Russian] 318 (2004), 5-13;
    • (2004) Zap. Nauchn. Semin. POMI , vol.318 , pp. 5-13
    • Arkhipova, A.1
  • 17
    • 0000496328 scopus 로고
    • Non linear elliptic systems with quadratic growth
    • M. Giaquinta and E. Giusti, "Non linear elliptic systems with quadratic growth," Manuscripta Math. 24 (1978), 323-349.
    • (1978) Manuscripta Math , vol.24 , pp. 323-349
    • Giaquinta, M.1    Giusti, E.2
  • 18
    • 0031643979 scopus 로고    scopus 로고
    • A new partial regularity proof for solutions of nonlinear elliptic systems
    • C. Hamburger, "A new partial regularity proof for solutions of nonlinear elliptic systems," Manuscripta Math. 95 (1998), 11-31.
    • (1998) Manuscripta Math , vol.95 , pp. 11-31
    • Hamburger, C.1
  • 19
    • 0034555619 scopus 로고    scopus 로고
    • Optimal interior partial regularity for nonlinear elliptic systems: The method of A-harmonic approximation
    • F. Duzaar and J. Grotowski, "Optimal interior partial regularity for nonlinear elliptic systems: the method of A-harmonic approximation," Manuscripta Math. 103 (2000), 267-298.
    • (2000) Manuscripta Math , vol.103 , pp. 267-298
    • Duzaar, F.1    Grotowski, J.2
  • 20
    • 33746579457 scopus 로고
    • On the regularity of the solutions of boundary-value problem for quasilinear elliptic systems with quadratic nonlinearity [in Russian]
    • A. Arkhipova, "On the regularity of the solutions of boundary-value problem for quasilinear elliptic systems with quadratic nonlinearity" [in Russian], Probl. Mat. Anal. 15 (1995), 47-69;
    • (1995) Probl. Mat. Anal , vol.15 , pp. 47-69
    • Arkhipova, A.1
  • 22
    • 0002521307 scopus 로고
    • Existence and partial regularity results for the heat flow for harmonic maps
    • Y. Chen and M. Struwe, "Existence and partial regularity results for the heat flow for harmonic maps," Math. Z. 201 (1989), 83-103.
    • (1989) Math. Z , vol.201 , pp. 83-103
    • Chen, Y.1    Struwe, M.2
  • 23
    • 0001920911 scopus 로고
    • Capacity methods in the theory of partial differential equations
    • J. Frehse, "Capacity methods in the theory of partial differential equations," Jahresber. Deutsch. Math.-Verein. 84 (1982), no. 1, 1-44.
    • (1982) Jahresber. Deutsch. Math.-Verein , vol.84 , Issue.1 , pp. 1-44
    • Frehse, J.1
  • 24
    • 84887241983 scopus 로고    scopus 로고
    • Quasilinear Hölder inequalities and a priori estimates for quasilinear elliptic systems
    • A. Arkhipova, "Quasilinear Hölder inequalities and a priori estimates for quasilinear elliptic systems," Rend. Mat. Acc. Lincei 14 (2003), no. 9, 91-108.
    • (2003) Rend. Mat. Acc. Lincei , vol.14 , Issue.9 , pp. 91-108
    • Arkhipova, A.1
  • 25
    • 29144507096 scopus 로고    scopus 로고
    • Near-boundary a priori estimates for solutions of nondiagonal elliptic systems with strong nonlinearity [in Russian]
    • A. Arkhipova, Near-boundary a priori estimates for solutions of nondiagonal elliptic systems with strong nonlinearity" [in Russian], Izv. Ross. Akad. Nauk Ser. Mat. 68 (2003), no. 2, 23-38;
    • (2003) Izv. Ross. Akad. Nauk Ser. Mat , vol.68 , Issue.2 , pp. 23-38
    • Arkhipova, A.1
  • 26
    • 33846969352 scopus 로고    scopus 로고
    • English transl.: Izv. Math. 68 (2003), no. 2, 243-258.
    • (2003) Izv. Math , vol.68 , Issue.2 , pp. 243-258
    • English transl1
  • 27
    • 0002104157 scopus 로고
    • Partial regularity for stationary harmonic maps into spheres
    • L. C. Evans, "Partial regularity for stationary harmonic maps into spheres," Arch. Rational Mech. Anal. 116 (1991), 101-113.
    • (1991) Arch. Rational Mech. Anal , vol.116 , pp. 101-113
    • Evans, L.C.1
  • 28
    • 0000738731 scopus 로고
    • On the singular set of stationary harmonic maps
    • F. Bethuel, "On the singular set of stationary harmonic maps," Manuscripta Math. 78 (1993), 417-443.
    • (1993) Manuscripta Math , vol.78 , pp. 417-443
    • Bethuel, F.1
  • 29
    • 0000301066 scopus 로고
    • Everywhere discontinuous harmonic maps into spheres
    • T. Rivière, "Everywhere discontinuous harmonic maps into spheres," Arch. Rational Mech. Anal. 175 (1995), 197-226.
    • (1995) Arch. Rational Mech. Anal , vol.175 , pp. 197-226
    • Rivière, T.1
  • 31
    • 0009326383 scopus 로고
    • Partial regularity for minimizers of certain functionals having nonquadratic growth
    • N. Fusco and J. Hutchinson, "Partial regularity for minimizers of certain functionals having nonquadratic growth," Ann. Mat. Pura Appl. (IV), CLV (1989), 1-24.
    • (1989) Ann. Mat. Pura Appl. (IV) , vol.155 , pp. 1-24
    • Fusco, N.1    Hutchinson, J.2
  • 32
    • 29144454979 scopus 로고    scopus 로고
    • Partial regularity of the minimizers of quadratic functionals with VMO coefficients
    • M. Ragusaand and A. Tachikawa, "Partial regularity of the minimizers of quadratic functionals with VMO coefficients," J. London Math. Soc. 72 (2005), no. 2, 609-620.
    • (2005) J. London Math. Soc , vol.72 , Issue.2 , pp. 609-620
    • Ragusaand, M.1    Tachikawa, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.