Let be a fixed integer. Given a smooth bounded, convex domain and a convex, even, and -homogeneous function of class for which the Hessian matrix is positive definite in for any , we study the monotonicity of the principal frequency of the anisotropic -Laplacian (constructed using the function ) on with respect to . As an application, we find a new variational characterization for the principal frequency on domains having a sufficiently small inradius. In the particular case where is the Euclidean norm in , we recover some recent results obtained by the first two authors in [3, 4].
Accepted:
Published online:
Marian Bocea 1; Mihai Mihăilescu 2, 3; Denisa Stancu-Dumitru 4
@article{CRMATH_2022__360_G9_993_0, author = {Marian Bocea and Mihai Mih\u{a}ilescu and Denisa Stancu-Dumitru}, title = {The {Monotonicity} of the {Principal} {Frequency} of the {Anisotropic} $p${-Laplacian}}, journal = {Comptes Rendus. Math\'ematique}, pages = {993--1000}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, year = {2022}, doi = {10.5802/crmath.348}, language = {en}, }
TY - JOUR AU - Marian Bocea AU - Mihai Mihăilescu AU - Denisa Stancu-Dumitru TI - The Monotonicity of the Principal Frequency of the Anisotropic $p$-Laplacian JO - Comptes Rendus. Mathématique PY - 2022 SP - 993 EP - 1000 VL - 360 PB - Académie des sciences, Paris DO - 10.5802/crmath.348 LA - en ID - CRMATH_2022__360_G9_993_0 ER -
%0 Journal Article %A Marian Bocea %A Mihai Mihăilescu %A Denisa Stancu-Dumitru %T The Monotonicity of the Principal Frequency of the Anisotropic $p$-Laplacian %J Comptes Rendus. Mathématique %D 2022 %P 993-1000 %V 360 %I Académie des sciences, Paris %R 10.5802/crmath.348 %G en %F CRMATH_2022__360_G9_993_0
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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