Taiwanese Journal of Mathematics

Strict Monotonicity and Unique Continuation for General Non-local Eigenvalue Problems

Silvia Frassu and Antonio Iannizzotto

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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.

Article information

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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Digital Object Identifier

Primary: 35R11: Fractional partial differential equations 35B60: Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx] 47A75: Eigenvalue problems [See also 47J10, 49R05]

non-local operators eigenvalue problems unique continuation


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

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