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The Monotonicity of the Principal Frequency of the Anisotropic p-Laplacian
Comptes Rendus. Mathématique, Tome 360 (2022) no. G9, pp. 993-1000.

Let D>1 be a fixed integer. Given a smooth bounded, convex domain Ω D and H: D [0,) a convex, even, and 1-homogeneous function of class C 3,α ( D {0}) for which the Hessian matrix D 2 (H p ) is positive definite in D {0} for any p(1,), we study the monotonicity of the principal frequency of the anisotropic p-Laplacian (constructed using the function H) on Ω with respect to p(1,). As an application, we find a new variational characterization for the principal frequency on domains Ω having a sufficiently small inradius. In the particular case where H is the Euclidean norm in D , we recover some recent results obtained by the first two authors in [3, 4].

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DOI : 10.5802/crmath.348
Classification : 35P30, 47J10, 49R05, 49J40, 58C40
Bocea, Marian 1 ; Mihăilescu, Mihai 2, 3 ; Stancu-Dumitru, Denisa 4

1 Division of Mathematical Sciences, National Science Foundation, 2415 Eisenhower Avenue, Alexandria, VA 22314 U.S.A.
2 Department of Mathematics, University of Craiova, 200585 Craiova, Romania
3 “Gheorghe Mihoc - Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania
4 Department of Mathematics and Computer Science, Politehnica University of Bucharest, 060042 Bucharest, Romania
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Bocea, Marian; Mihăilescu, Mihai; Stancu-Dumitru, Denisa. The Monotonicity of the Principal Frequency of the Anisotropic $p$-Laplacian. Comptes Rendus. Mathématique, Tome 360 (2022) no. G9, pp. 993-1000. doi : 10.5802/crmath.348. http://www.numdam.org/articles/10.5802/crmath.348/

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