Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

The interval of resolvent-positivity for the biharmonic operator

Author(s): Michael Ulm
Journal: Proc. Amer. Math. Soc. 127 (1999), 481-489.
MSC (1991): Primary 34L40, 35B50, 47A10
MathSciNet review: 1468205
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Abstract: For an operator on a Banach lattice we examine the interval on the real line for which the resolvent $\left( \lambda - A \right)^{-1}$ is positive. This positivity interval is then explicitly calculated for the biharmonic operator with three different boundary conditions.

References:

1.: W. Arendt, C. J. K. Batty, and D. W. Robinson, Positive semigroups generated by elliptic operators on Lie groups, J. Operator Theory 23 (1990), 369 - 407. MR 91k:47118
2.: C. V. Coffman, On the structure of solutions to $\Delta^2 u = \lambda u$ which satisfy the clamped plate condition on a right angle, SIAM J. Math. Anal. 13 (1982), 746 - 757. MR 84a:35015
3.: R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo 1988 MR 89m:00001
4.: G. Greiner, J. Voigt, and M.P.H. Wolff, On the spectral bound of the generator of semigroups of positive operators, J. Operator Theory 5 (1981), 245 - 256. MR 82h:47039
5.: H.-C. Grunau and G. Sweers, Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions, TWI report 95-56, TU Delft, 1995; Math. Ann. 307 (1997), 589-626. CMP 97:16
6.: V. A. Kozlov, V. A. Kondrat'ev, and V. G. Maz'ya, On sign variations and the absence of "strong" zeros of elliptic equations, Math. USSR Izvestiya 34 (1990), 337 - 353. MR 90i:35021

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