Denisa Stancu-Dumitru
University Politehnica of Bucharest & University of Bucharest ICUB Research Group, Bucharest, Romania

For a smooth bounded, convex domain $\Omega \subset \mathbb R^D (D\geq 2)$ and $H:\mathbb R^D\rightarrow[0,\infty)$ a convex, even, and $1$-homogeneous function of class $C^{3,\alpha}(\mathbb R^D\setminus\{0\})$ for which the Hessian matrix $D^2(H^p)$ is positive definite in $\mathbb R^D\setminus\{0\}$ for any $p\in(1,\infty)$, we study the monotonicity of the principal frequency of the anisotropic $p$-Laplacian, constructed using the function $H$, on $\Omega$ with respect to $p\in(1,\infty)$. As an application, we find a new variational characterization for the principal frequency on domains $\Omega$ having a sufficiently small inradius.

This is a joint work with Marian Bocea and Mihai Mihăilescu. This presentation is partially supported by CNCS-UEFISCDI Grant No. PN-III-P1-1.1-TE-2021-1539.