Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 24, Number 3 (2020), 681-694.
Strict Monotonicity and Unique Continuation for General Non-local Eigenvalue Problems
We consider the weighted eigenvalue problem for a general non-local pseudo-differential operator, depending on a bounded weight function. For such problem, we prove that strict (decreasing) monotonicity of the eigenvalues with respect to the weight function is equivalent to the unique continuation property of eigenfunctions. In addition, we discuss some unique continuation results for the special case of the fractional Laplacian.
Taiwanese J. Math., Volume 24, Number 3 (2020), 681-694.
Received: 28 May 2019
Revised: 2 July 2019
Accepted: 30 July 2019
First available in Project Euclid: 19 May 2020
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Frassu, Silvia; Iannizzotto, Antonio. Strict Monotonicity and Unique Continuation for General Non-local Eigenvalue Problems. Taiwanese J. Math. 24 (2020), no. 3, 681--694. doi:10.11650/tjm/190709. https://projecteuclid.org/euclid.twjm/1589875224