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arXiv · 1808.09368

Strict monotonicity and unique continuation for general non-local eigenvalue problems

Silvia Frassu·Antonio Iannizzotto
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Abstract

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.

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Silvia Frassu, Antonio Iannizzotto. 2018-08-28. Strict monotonicity and unique continuation for general non-local eigenvalue problems. https://arxiv.org/abs/1808.09368

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