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March  2005, 4(1): 101-114. doi: 10.3934/cpaa.2005.4.101

The Faber--Krahn inequality for random/nonautonomous parabolic equations

Janusz Mierczyński 1, and  Wenxian Shen 2,

1. 

Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, PL-50-370 Wrocław, Poland
2. 

Department of Mathematics, Auburn University, AL 36849-5310

Received  May 2004 Revised  November 2004 Published  December 2004

The paper extends the Faber--Krahn inequality for elliptic and periodic parabolic problems to random and general nonautonomous parabolic problems. Under proper assumptions, it also provides necessary and sufficient conditions for the Faber-Krahn inequality being equality.
Keywords: Schwarz symmetrization, The Faber--Krahn inequality, principal Lyapunov exponent, recurrent function., principal spectrum, Schwarz symmetrized domain.
Mathematics Subject Classification: 35K20, 35P15, 37H1.
Citation: Janusz Mierczyński, Wenxian Shen. The Faber--Krahn inequality for random/nonautonomous parabolic equations. Communications on Pure and Applied Analysis, 2005, 4 (1) : 101-114. doi: 10.3934/cpaa.2005.4.101
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