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12 September 2002 On principal eigenvalues for periodic parabolic Steklov problems
T. Godoy, E. Lami Dozo, S. Paczka
Abstr. Appl. Anal. 7(8): 401-421 (12 September 2002). DOI: 10.1155/S1085337502204066


Let Ω be a C2+γ domain in N, N2, 0<γ<1. Let T>0 and let L be a uniformly parabolic operator Lu=u/ti,j(/xi)(aij(u/xj))+jbj(u/xi)+a0u, a00, whose coefficients, depending on (x,t)Ω×, are T periodic in t and satisfy some regularity assumptions. Let A be the N×N matrix whose i,j entry is aij and let ν be the unit exterior normal to Ω. Let m be a T-periodic function (that may change sign) defined on Ω whose restriction to Ω× belongs to Wq21/q,11/2q(Ω×(0,T)) for some large enough q. In this paper, we give necessary and sufficient conditions on m for the existence of principal eigenvalues for the periodic parabolic Steklov problem Lu=0 on Ω×, Au,ν=λmu on Ω×, u(x,t)=u(x,t+T), u>0 on Ω×. Uniqueness and simplicity of the positive principal eigenvalue is proved and a related maximum principle is given.


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T. Godoy. E. Lami Dozo. S. Paczka. "On principal eigenvalues for periodic parabolic Steklov problems." Abstr. Appl. Anal. 7 (8) 401 - 421, 12 September 2002.


Published: 12 September 2002
First available in Project Euclid: 14 April 2003

zbMATH: 1014.35038
MathSciNet: MR1930825
Digital Object Identifier: 10.1155/S1085337502204066

Primary: 35K20 , 35P05
Secondary: 35B10 , 35B50

Rights: Copyright © 2002 Hindawi

Vol.7 • No. 8 • 12 September 2002
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