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The Faber-Krahn inequality for random/nonautonomous parabolic equations. (English) Zbl 1194.35520
Summary: 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.

MSC:
35R60 PDEs with randomness, stochastic partial differential equations
35K20 Initial-boundary value problems for second-order parabolic equations
35P15 Estimates of eigenvalues in context of PDEs
37H15 Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents
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