Fundamental solution, eigenvalue asymptotics and eigenfunctions of degenerate elliptic operators with positive potentials
Kazuhiro Kurata; Satoko Sugano
Studia Mathematica (2000)
- Volume: 138, Issue: 2, page 101-119
- ISSN: 0039-3223
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topKurata, Kazuhiro, and Sugano, Satoko. "Fundamental solution, eigenvalue asymptotics and eigenfunctions of degenerate elliptic operators with positive potentials." Studia Mathematica 138.2 (2000): 101-119. <http://eudml.org/doc/216693>.
@article{Kurata2000,
abstract = {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.},
author = {Kurata, Kazuhiro, Sugano, Satoko},
journal = {Studia Mathematica},
keywords = {elliptic equations; fundamental solution; eigenvalue; eigenfunctions},
language = {eng},
number = {2},
pages = {101-119},
title = {Fundamental solution, eigenvalue asymptotics and eigenfunctions of degenerate elliptic operators with positive potentials},
url = {http://eudml.org/doc/216693},
volume = {138},
year = {2000},
}
TY - JOUR
AU - Kurata, Kazuhiro
AU - Sugano, Satoko
TI - Fundamental solution, eigenvalue asymptotics and eigenfunctions of degenerate elliptic operators with positive potentials
JO - Studia Mathematica
PY - 2000
VL - 138
IS - 2
SP - 101
EP - 119
AB - 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.
LA - eng
KW - elliptic equations; fundamental solution; eigenvalue; eigenfunctions
UR - http://eudml.org/doc/216693
ER -
References
top- [CSW] S. Chanillo, J. Strömberg and R. Wheeden, Norm inequalities for potential type operators, Rev. Mat. Iberoamericana 3 (1987), 311-335. Zbl0696.31010
- [CW] S. Chanillo and R. L. Wheeden, Existence and estimates of Green's function for degenerate elliptic equations, Ann. Scuola Norm. Sup. Pisa 15 (1988), 309-340. Zbl0688.35002
- [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. Zbl0626.35022
- [CF] F. Chiarenza and M. Frasca, Morrey spaces and Hardy-Littlewood maximal function, Rend. Mat. 7 (1987), 273-279. Zbl0717.42023
- [CoF] R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250. Zbl0291.44007
- [Da] E. B. Davies, Heat Kernels and Spectral Theory, Cambridge Univ. Press, 1989. Zbl0699.35006
- [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. Zbl0488.35034
- [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. Zbl0498.35042
- [Fe] C. Fefferman, The uncertainty principle, Bull. Amer. Math. Soc. 9 (1983), 129-206. Zbl0526.35080
- [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 -integrability of the partial derivatives of a quasi-conformal mapping, Acta Math. 130 (1973), 265-277. Zbl0258.30021
- [Gu] C. Gutiérrez, Harnack's inequality for degenerate Schrödinger operators, Trans. Amer. Math. Soc. 312 (1989), 403-419. Zbl0685.35020
- [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. Zbl0805.35017
- [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 spaces and Morrey spacs, Math. Nachr., to appear. Zbl0939.35036
- [Mu] M. Murata, On construction of Martin boundaries for second order elliptic equations, Publ. Res. Inst. Math. Sci. 26 (1990), 585-627. Zbl0726.31009
- [Sh1] Z. Shen, estimates for Schrödinger operators with certain potentials, Ann. Inst. Fourier (Grenoble) 45 (1995), 513-546. Zbl0818.35021
- [Sh2] Z. Shen, Eigenvalue asymptotics and exponential decay of eigenfunctions for Schrödinger operators with magnetic fields, Trans. Amer. Math. Soc. 348 (1996), 4465-4488. Zbl0866.35088
- [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 and spaces, Trans. Amer. Math. Soc. 287 (1985), 293-321.
- [Su] S. Sugano, Estimates for the operators and 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. Zbl0726.35091
- [Zh] J. Zhong, Harmonic analysis for some Schrödinger type operators, Ph.D. thesis, Princeton Univ., 1993.
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