期刊
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
卷 58, 期 1, 页码 85-103出版社
SIAM PUBLICATIONS
DOI: 10.1137/18M1218704
关键词
principal eigenvalue; (Agmon) ground state; semilinear PDE; Donsker-Varadhan functional; Collatz-Wielandt formula; min-max formula
资金
- National Science Foundation [DMS-1715210]
- Army Research Office [W911NF17-1-001]
- Office of Naval Research [N00014-16-1-2956]
- INSPIRE faculty fellowship
- DST-SERB grant [EMR/2016/004810]
We address the variational problem for the generalized principal eigenvalue on R-d of linear and semilinear elliptic operators associated with nondegenerate diffusions controlled through the drift. We establish the Collatz-Wielandt formula for potentials that vanish at infinity under minimal hypotheses, and also for general potentials under blanket geometric ergodicity assumptions. We also present associated results having the flavor of a refined maximum principle.
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