Extremal properties of the first eigenvalue of a class of elliptic eigenvalue problems

Henrik Egnell

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1987)

  • Volume: 14, Issue: 1, page 1-48
  • ISSN: 0391-173X

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Egnell, Henrik. "Extremal properties of the first eigenvalue of a class of elliptic eigenvalue problems." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 14.1 (1987): 1-48. <http://eudml.org/doc/83998>.

@article{Egnell1987,
author = {Egnell, Henrik},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {first eigenvalue; zero boundary data; maximizing the first eigenvalue; weighted -ball; minimizing the first eigenvalue},
language = {eng},
number = {1},
pages = {1-48},
publisher = {Scuola normale superiore},
title = {Extremal properties of the first eigenvalue of a class of elliptic eigenvalue problems},
url = {http://eudml.org/doc/83998},
volume = {14},
year = {1987},
}

TY - JOUR
AU - Egnell, Henrik
TI - Extremal properties of the first eigenvalue of a class of elliptic eigenvalue problems
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1987
PB - Scuola normale superiore
VL - 14
IS - 1
SP - 1
EP - 48
LA - eng
KW - first eigenvalue; zero boundary data; maximizing the first eigenvalue; weighted -ball; minimizing the first eigenvalue
UR - http://eudml.org/doc/83998
ER -

References

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  2. [AH] M.S. Ashbaugh, E.M. HarrellII, Maximal and Minimal Eigenvalues and their Associated Nonlinear Equations. Preprint. 
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  4. [BN] H. Brezis, L. Nirenberg, Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents. Comm. Pure Appl. Math., 4 (1983), pp. 437-477. Zbl0541.35029MR709644
  5. [ES] M. Essén, Optimization and Rearrangements of the Coefficients in the Differential Equation(s) y'' ± qy = 0, Math. Rep. Canad. Acad. Sci. VI (1), pp. 15-20, 1984. Zbl0532.34026MR734067
  6. — Optimization and Rearrangements of the Coefficients in the Operator d 2/dt2-p(t)2 on a Finite Interval, J. Math. Anal. Appl., 115 (1986), pp. 278-304. Zbl0603.34060MR835601
  7. — Optimization and α-disfocality for Ordinary Differential Equations, Canad. J. Math. 2 (1985), pp. 310-323. Zbl0553.34022
  8. [GT] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1977. Zbl0361.35003MR473443
  9. [HA] E.M. HarrellII, Hamiltonian Operators with Maximal Eigenvalues, J. Math. Phys.25 (1984), pp. 48-51. Zbl0555.35098MR728885
  10. [HL] G.H. Hardy, J.E. Littlewood, G. Pólya, Inequalities, Cambridge University Press, 1934. Zbl0010.10703
  11. [KS] D. Kinderlehrer, G. Stampacchia, An Introduction to Variational Inequalities and their Applications, Academic Press, New York, 1980. Zbl0457.35001MR567696
  12. [MO] C.B. MorreyJr., Multiple Integrals in the Calculus of Variations, Springer-Verlag, 1966. Zbl0142.38701MR202511
  13. [NI] L. Nirenberg, Topics in Nonlinear Functional Analysis, Courant Institute of Mathematical Sciences, 1974. Zbl0286.47037MR488102
  14. [RA] A.G. Ramm, Questions 5 in Part 2, Notices Amer. Math. Soc., 29 (1982), pp. 328-329. 
  15. [ST] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970. Zbl0207.13501MR290095
  16. [TA] G. Talenti, Estimates for Eigenvalues of Sturm-Liouville Problems, General Inequalities 4 (Edited by W. Walter), pp. 341-350, Birkäuser, 1984. Zbl0591.34019MR821811
  17. [WE] J. Weidmann, Linear Operators in Hilbert Spaces, Springer-Verlag, 1980. Zbl0434.47001MR566954
  18. [HA] E.M. HarrellII, Erratum: Hamiltonian Operators with maximal eigenvalues, J. Math. Phys.27 (1986), p. 419. Zbl0555.35098MR816465

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