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Monotonicity of the principal eigenvalue of the
 -Laplacian in an annulus
Author(s):
B.
Emamizadeh;
M.
Zivari-Rezapour
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1725-1731.
MSC (2000):
Primary 35P30
Posted:
December 18, 2007
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Abstract:
In this note we prove a monotonicity result related to the principal eigenvalue of the  -Laplacian in an annulus in  .
References:
-
- 1.
- L. Damascelli, Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results, Ann. Inst. Henri Poincaré, vol. 15, n. 4, 1998, p. 493-516. MR 1632933 (99e:35081)
- 2.
- M. Otani and T. Teshima, On the first eigenvalue of some quasilinear elliptic equations, Proc. Japan Acad. Ser. A Math. Sci., Vol. 64, no. 1, 1988, p. 8-10. MR 953752 (89h:35257)
- 3.
- A.G. Ramm and P.N. Shivakumar, Inequalities for the minimal eigenvalue of the Laplacian in an annulus, Math. Inequal. Appl., Vol. 1, n. 4, 1998, p. 559-563. MR 1646670 (99f:35149)
- 4.
- J. Simon, Differentiation with respect to the domain in boundary value problems, Numer. Funct. Anal. and Optimiz., Vol. 2(7&8), 1980, p. 649-687. MR 619172 (83m:49032)
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Additional Information:
B.
Emamizadeh
Affiliation:
Department of Mathematics,The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates
Email:
bemamizadeh@pi.ac.ae
M.
Zivari-Rezapour
Affiliation:
Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
Email:
m_zivari@iust.ac.ir
DOI:
10.1090/S0002-9939-07-09153-8
PII:
S 0002-9939(07)09153-8
Keywords:
$p$-Laplacian,
principal eigenvalue,
domain derivative
Received by editor(s):
December 13, 2006
Received by editor(s) in revised form:
February 19, 2007 and February 28, 2007
Posted:
December 18, 2007
Communicated by:
Walter Craig
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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