메뉴 건너뛰기




Volumn 350, Issue 5, 1998, Pages 2105-2128

Minimizing the Laplacian of a function squared with prescribed values on interior boundariestheory of polysplines

Author keywords

A priori estimates; Multivariate splines; Polyharmonic functions; Variational problem

Indexed keywords


EID: 22044447135     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-98-01961-8     Document Type: Article
Times cited : (13)

References (25)
  • 1
    • 0003796630 scopus 로고
    • Academic Press, New York, MR 56:9247
    • [Adams] R. A. Adams, Sobolev spaces, Academic Press, New York, 1975. MR 56:9247
    • (1975) Sobolev Spaces
    • Adams, R.A.1
  • 5
    • 0002161735 scopus 로고
    • Machine contouring using minimum curvature
    • [Bri] J.C. Briggs, Machine contouring using minimum curvature, Geophysics, 39 (1974), 39-48.
    • (1974) Geophysics , vol.39 , pp. 39-48
    • Briggs, J.C.1
  • 6
    • 0017216638 scopus 로고
    • Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces
    • MR 57:10315
    • [Du] J. Duchon, Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces, R.A.I.R.O. Analyse Numérique, vol. 10, no. R-3 (1976), pp. 5-12. MR 57:10315
    • (1976) R.A.I.R.O. Analyse Numérique , vol.10 , Issue.3 , pp. 5-12
    • Duchon, J.1
  • 8
    • 0022210631 scopus 로고
    • Splines in geophysics
    • [GA] P. Gonzalez-Casanova and R. Alvarez, Splines in geophysics, Geophysics, 50, No. 12 (1985), 2831-2848.
    • (1985) Geophysics , vol.50 , Issue.12 , pp. 2831-2848
    • Gonzalez-Casanova, P.1    Alvarez, R.2
  • 9
    • 0003668851 scopus 로고
    • PseudoDifferential Operators, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, MR 87d:35002a
    • [H] L. Hörmander, The Analysis of Linear Partial Differential Operators III. PseudoDifferential Operators, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1985. MR 87d:35002a
    • (1985) The Analysis of Linear Partial Differential Operators III
    • Hörmander, L.1
  • 10
    • 0040610260 scopus 로고
    • Peano theorem for linear functionals vanishing on polyharmonic functions
    • Charles Chui and L. Schumaker (eds.), World Scientific Publishing Co.
    • [HK] W. Haussmann, O.I. Kounchev, Peano theorem for linear functionals vanishing on polyharmonic functions, In: Approximation Theory VIII, Vol. 1, Charles Chui and L. Schumaker (eds.), World Scientific Publishing Co., 1995, pp. 233-240.
    • (1995) Approximation Theory VIII , vol.1 , pp. 233-240
    • Haussmann, W.1    Kounchev, O.I.2
  • 11
    • 0742301357 scopus 로고
    • Definition and basic properties of polysplines, I and II
    • No. 8, pp. 13-16. MR 93a:41016; MR 92m:41031
    • [Kol] O.I. Kounchev, Definition and basic properties of polysplines, I and II, C. R. Acad. Bulg. Sei., 44 (1991), No. 7, pp. 9-11; No. 8, pp. 13-16. MR 93a:41016; MR 92m:41031
    • (1991) C. R. Acad. Bulg. Sei. , vol.44 , Issue.7 , pp. 9-11
    • Kounchev, O.I.1
  • 14
    • 33646902105 scopus 로고
    • Splines constructed by pieces of polyharmonic functions
    • Eds. P.-J. Laurent et al., AK Peters, Mass.
    • [Ko4] O. I. Kounchev, Splines constructed by pieces of polyharmonic functions, In: Wavelets, Images and Surface Fitting, Eds. P.-J. Laurent et al., AK Peters, Mass., 1994, pp. 319-326.
    • (1994) Wavelets, Images and Surface Fitting , pp. 319-326
    • Kounchev, O.I.1
  • 15
    • 33646902369 scopus 로고
    • Minimizing the integral of the Laplacian of a function suqared with prescribed values on interior boundaries - Theory of polysplines
    • [Ko5] O.I. Kounchev, Minimizing the integral of the Laplacian of a function suqared with prescribed values on interior boundaries - theory of polysplines, I, University of Duisburg, preprint SM-DU-211,1993.
    • (1993) I, University of Duisburg, Preprint SM-DU-211
    • Kounchev, O.I.1
  • 16
    • 0004223510 scopus 로고
    • Hermann, Paris, 1972. Russian transi. "Mir", Moscow, MR 57:6947
    • [Laur] P.-J, Laurent, Approximation et Optimisation. Hermann, Paris, 1972. (Russian transi. "Mir", Moscow, 1975) MR 57:6947
    • (1975) Approximation Et Optimisation
    • Laurent, P.-J.1
  • 18
    • 38249020082 scopus 로고
    • Polyharmonic cardinal splines
    • MR 91j:41022
    • [Ma] W. R. Madych, Polyharmonic cardinal splines, Jour. Approx. Theory, 60 (1990), No. 2, 141-156. MR 91j:41022
    • (1990) Jour. Approx. Theory , vol.60 , Issue.2 , pp. 141-156
    • Madych, W.R.1
  • 19
    • 0003953931 scopus 로고
    • The Problem of the Minimum of a Quadratic Functional
    • English transi. Holden-Day, Inc., San Francisco, London, Amsterdam, MR 16:41b; MR 30:1427
    • [Mikh] S. Mikhlin, The Problem of the Minimum of a Quadratic Functional, GITTL, MoscowLeningrad, 1952 (English transi. Holden-Day, Inc., San Francisco, London, Amsterdam, 1965) MR 16:41b; MR 30:1427
    • (1965) GITTL, MoscowLeningrad, 1952
    • Mikhlin, S.1
  • 21
    • 0004016842 scopus 로고
    • J. Wiley and Sons, N.Y., ChichesterBrisbane-Toronto, MR 82j:41001
    • [Schum] L. L. Schumaker, Spline Functions: Basic Theory, J. Wiley and Sons, N.Y., ChichesterBrisbane-Toronto, 1981. MR 82j:41001
    • (1981) Spline Functions: Basic Theory
    • Schumaker, L.L.1
  • 22
    • 0004100833 scopus 로고
    • Paris: Hermann (2nd ed., Ann. Inst. Fourier (Grenoble) 7 (1957), 1-141; 8 (1958), 1-209). MR 12:31d; MR 12:833d; MR 21:6534; MR 22:8322
    • [Schw] L. Schwartz, Théorie des distributions, vols. 1,11, Paris: Hermann 1950-51 (2nd ed., Ann. Inst. Fourier (Grenoble) 7 (1957), 1-141; 8 (1958), 1-209). MR 12:31d; MR 12:833d; MR 21:6534; MR 22:8322
    • (1950) Théorie Des Distributions , vol.1-11
    • Schwartz, L.1
  • 23
    • 0025255746 scopus 로고
    • Gridding with continuous curvature splines intension
    • [Smi] M. H. F. Smith, P. Wessel, Gridding with continuous curvature splines intension, Geophysics, 55 (1990), No. 3, 293-305.
    • (1990) Geophysics , vol.55 , Issue.3 , pp. 293-305
    • Smith, M.H.F.1    Wessel, P.2
  • 24
    • 0003785339 scopus 로고
    • Moscow, 1948 English transi., North-Holland, Amsterdam, and Wiley, New York, MR ll:598a; MR 35:3243
    • [Vek] I. N. Vekua, New Methods for Solving Elliptic Equations, OGIZ, Moscow, 1948 (English transi., North-Holland, Amsterdam, and Wiley, New York, 1967). MR ll:598a; MR 35:3243
    • (1967) New Methods for Solving Elliptic Equations, OGIZ
    • Vekua, I.N.1
  • 25
    • 0001388356 scopus 로고
    • Surface fitting with scattered noisy data in Euclidean d-space and on the sphere
    • Winter MR 86c:65017
    • [Wa] G. Wahba, Surface fitting with scattered noisy data in Euclidean d-space and on the sphere, Rocky Mount. J. Math., 14 (Winter 1984), No. 1, pp. 281-299. MR 86c:65017
    • (1984) Rocky Mount. J. Math. , vol.14 , Issue.1 , pp. 281-299
    • Wahba, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.