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2000 | 138 | 2 | 101-119
Tytuł artykułu

Fundamental solution, eigenvalue asymptotics and eigenfunctions of degenerate elliptic operators with positive potentials

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show a weighted version of Fefferman-Phong's inequality and apply it to give an estimate of fundamental solutions, eigenvalue asymptotics and exponential decay of eigenfunctions for certain degenerate elliptic operators of second order with positive potentials.
Słowa kluczowe
Czasopismo
Rocznik
Tom
138
Numer
2
Strony
101-119
Opis fizyczny
Daty
wydano
2000
otrzymano
1997-12-31
poprawiono
1999-10-13
poprawiono
1999-11-20
Twórcy
  • Kazuhiro Kurata, Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo, 192-03 Japan, kurata@comp.metro-u.ac.jp
Bibliografia
  • [CSW] S. Chanillo, J. Strömberg and R. Wheeden, Norm inequalities for potential type operators, Rev. Mat. Iberoamericana 3 (1987), 311-335.
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  • [CFG] F. Chiarenza, E. Fabes and N. Garofalo, Harnack's inequality for Schrödinger operators and the continuity of solutions, Proc. Amer. Math. Soc. 98 (1986), 415-425.
  • [CF] F. Chiarenza and M. Frasca, Morrey spaces and Hardy-Littlewood maximal function, Rend. Mat. 7 (1987), 273-279.
  • [CoF] R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250.
  • [Da] E. B. Davies, Heat Kernels and Spectral Theory, Cambridge Univ. Press, 1989.
  • [FJK] E. Fabes, D. Jerison and C. Kenig, The Wiener test for degenerate elliptic equations, Ann. Inst. Fourier (Grenoble) 32 (1982), no. 3, 151-182.
  • [FKS] E. Fabes, C. Kenig and R. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations 7 (1982), 77-116.
  • [Fe] C. Fefferman, The uncertainty principle, Bull. Amer. Math. Soc. 9 (1983), 129-206.
  • [GR] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. Stud. 116, North-Holland, 1985.
  • [Ge] F. Gehring, The $L^p$-integrability of the partial derivatives of a quasi-conformal mapping, Acta Math. 130 (1973), 265-277.
  • [Gu] C. Gutiérrez, Harnack's inequality for degenerate Schrödinger operators, Trans. Amer. Math. Soc. 312 (1989), 403-419.
  • [Hö] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, 1983.
  • [Ku1] K. Kurata, Continuity and Harnack's inequality for solutions of elliptic partial differential equations of second order, Indiana Univ. Math. J. 43 (1994), 411-440.
  • [Ku2] K. Kurata, On doubling properties for non-negative weak solutions of elliptic and parabolic PDE, Israel J. Math., to appear.
  • [KS] K. Kurata and S. Sugano, A remark on estimates for uniformly elliptic operators on weighted $L^p$ spaces and Morrey spacs, Math. Nachr., to appear.
  • [Mu] M. Murata, On construction of Martin boundaries for second order elliptic equations, Publ. Res. Inst. Math. Sci. 26 (1990), 585-627.
  • [Sh1] Z. Shen, $L^p$ estimates for Schrödinger operators with certain potentials, Ann. Inst. Fourier (Grenoble) 45 (1995), 513-546.
  • [Sh2] Z. Shen, Eigenvalue asymptotics and exponential decay of eigenfunctions for Schrödinger operators with magnetic fields, Trans. Amer. Math. Soc. 348 (1996), 4465-4488.
  • [Sm] H. F. Smith, Parametrix construction for a class of subelliptic differential operators, Duke Math. J. 63 (1991), 343-354.
  • [SW] J. O. Strömberg and R. L. Wheeden, Fractional integrals on weighted $H^p$ and $L^p$ spaces, Trans. Amer. Math. Soc. 287 (1985), 293-321.
  • [Su] S. Sugano, Estimates for the operators $V^α (-Δ +V)^-β$ and $V^α ᐁ (-Δ +V)^-β$ with certain nonnegative potentials V, Tokyo J. Math. 21 (1998), 441-452.
  • [Ta] K. Tachizawa, Asymptotic distribution of eigenvalues of Schrödinger operators with nonclassical potentials, Tôhoku Math. J. 42 (1990), 381-406.
  • [Zh] J. Zhong, Harmonic analysis for some Schrödinger type operators, Ph.D. thesis, Princeton Univ., 1993.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv138i2p101bwm
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