Abstract
The aim of this note is to present a new method deducing lower bounds for the first eigenvalue of a class of nonlinear Stokes eigenvalue problems. In [1] and [3] the linear Stokes eigenvalue problem is attributed to the Lame operator with a very large coefficient in front of the expression grad div u. In our book [2] we also refer to this connection. The method proposed here is basing on relations between the first eigenvalue of Dirichlet’s problem for the Laplace equation and the norm of the Vekua operator.
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References
Gürlebeck, K. (1988) ‘Lower and upper bounds for the first eigenvalue of the Lame’system’ to appear in: Proceedings of the Conference on Complex Analysis (GDR, Halle), Pitman, London.
Gürlebeck, K. and Sprüssig, W. (1989) ‘Quaternionic Analysis and Elliptic Boundary Value Problems’, Mathematical Research Bd. 53, Akademie-Verlag Berlin.
Kawohl, B and Sweers, G. (1987) ‘Remarks on eigenvalues and eigenfunctions of a special elliptic system’, J. Appl. Math. Phys. (ZAMP), Vol. 38, Sept. 1987, 730–740.
Levine, H. and Protter, M.H. (1985) ‘Unrestricted lower bounds for eigenvalues for classes of elliptic equations and systems of equations with application to problems in elasticity’, Math. Meth. Appl. Sci. 7, 210–222.
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© 1992 Springer Science+Business Media Dordrecht
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Sprossig, W., Gurlebeck, K. (1992). On eigenvalue estimates of nonlinear Stokes eigenvalue problems. In: Micali, A., Boudet, R., Helmstetter, J. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8090-8_32
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DOI: https://doi.org/10.1007/978-94-015-8090-8_32
Publisher Name: Springer, Dordrecht
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