Comptes Rendus
Partial differential equations
The Monotonicity of the Principal Frequency of the Anisotropic p-Laplacian
Comptes Rendus. Mathématique, Volume 360 (2022), 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
Marian Bocea 1; Mihai Mihăilescu 2, 3; Denisa Stancu-Dumitru 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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {The {Monotonicity} of the {Principal} {Frequency} of the {Anisotropic} $p${-Laplacian}},
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Marian Bocea; Mihai Mihăilescu; Denisa Stancu-Dumitru. The Monotonicity of the Principal Frequency of the Anisotropic $p$-Laplacian. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 993-1000. doi : 10.5802/crmath.348. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.348/

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