| Abstract: |
| We consider an eigenvalue problem for a local-nonlocal equation that includes the Laplace operator and a nonlocal operator with a regular kernel. A comprehensive analysis of the principal eigenvalue is performed, and several monotonicity properties are presented with respect to the domain and the kernel. In particular, we study the principal eigenvalue of the equation where the Laplace operator term is multiplied by epsilon. Finally, we analyze the convergence of the principal eigenvalue as epsilon goes to zero and as epsilon goes to infinity. |
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