Positivity preserving results for a biharmonic equation under Dirichlet boundary conditions

• Autorzy: Omrane H. B. , Khenissy S.

Identyfikatory

DOI

http://dx.doi.org/10.7494/OpMath.2014.34.3.601

• Języki publikacji: EN

Abstrakty

EN

We prove a dichotomy result giving the positivity preserving property for a biharmonic equation with Dirichlet boundary conditions arising in MEMS models. We adapt some ideas in [H.-Ch. Grunau, G. Sweers, Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions, Math. Ann. 307 (1997), 589–626].

Słowa kluczowe

EN

biharmonic equation; positivity preserving; Dirichlet problem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2014
• Tom: Vol. 34, no. 3
• Strony: 601--608
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Omrane H. B.

• Institut Préparatoire des Études d’Ingénierie de Tunis Mont-Fleury, Tunisie

autor

Khenissy S.

• Département de Mathématiques Appliquées Institut Supérieur d’Informatique, Ariana, Tunisie

Bibliografia

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• [3] H.-Ch. Grunau, Positivity, change of sign and buckling eigenvalues in a one-dimensional fourth order model problem, Adv. Differential Equations 7 (2002), 177–196.
• [4] H.-Ch. Grunau, G. Sweers, Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions, Math. Ann. 307 (1997), 589–626.
• [5] H.-Ch. Grunau, G. Sweers, Sign change for the Green function and for the first eigenfunction of equations of clamped-plate type, Arch. Rational Mech. Anal. 150 (1999), 179–190.
• [6] P. Laurençot, C. Walker, Sign-preserving property for some fourth oreder elliptic operators in one dimension and radial symmetry, J. Anal. Math., to appear.
• [7] F.H. Lin, Y.S. Yang, Nonlinear non-local elliptic equation modelling electrostatic actuation, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. A 463 (2007), 1323–1337.
• [8] J.A. Pelesko, D.H. Bernstein, Modelling MEMS and NEMS, New York, NY: Chapman & Hall/CRC, 2003