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On the limit behavior of the largest eigenvalue of an elliptic operator with a small parameter. (English. Russian original) Zbl 0598.35079
Math. USSR, Sb. 55, 529-545 (1986); translation from Mat. Sb., Nov. Ser. 127(169), No. 4, 538-554 (1985).
The author studies the asymptotic behaviour of the greatest eigenvalue of the elliptic operator \(L_ 0+\epsilon L_ 1\) for \(\epsilon\) tending to 0. Here \(L_ 0\), \(L_ 1\) are of second order and \(L_ 0\) may degenerate. Condition for the existence of the limit of the eigenvalue is given in terms of the probabilistic properties of the diffusion process generated by \(L_ 0\).
Reviewer: B.Nowak
35P15 Estimates of eigenvalues in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
60J99 Markov processes
35K05 Heat equation
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