Monotonicity results for the principal eigenvalue of the generalized Robin problem

By T. Giorgi, R. Smits. 2005

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Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities (2008, unknown): “We refer, for instance, to [2], [3], [4], [10], [12], [13], [14], [15], [17], [25], [26], [28], [29], [35], [37], [40], [52], and the literature cited therein.”
Faber–Krahn Inequalities for the Robin-Laplacian: A Free Discontinuity Approach (2015, background): “For instance, being the term of area type, rescaling properties under dilations are not available; moreover, since the competing functions are not necessarily zero at the boundary, λβ does not enjoy the natural monotonicity properties of λ D (see [19]).”