Related papers: Sharp estimates for the anisotropic torsional rigi…
A one-parameter family of variational problems is introduced that interpolates between torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. The associated partial differential equation is derived, which is shown to have…
In this paper we study optimal estimates for two functionals involving the anisotropic $p$-torsional rigidity $T_p(\Omega)$, $1<p<+\infty$. More precisely, we study $\Phi(\Omega)=\frac{T_p(\Omega)}{|\Omega|M(\Omega)}$ and…
We consider the torsional rigidity and the principal eigenvalue related to the $p$-Laplace operator. The goal is to find upper and lower bounds to products of suitable powers of the quantities above in various classes of domains. The limit…
We study torsional rigidity for graph and quantum graph analogs of well-known pairs of isospectral non-isometric planar domains. We prove that such isospectral pairs are distinguished by torsional rigidity.
Sharp lower and upper uniform estimates are obtained for fundamental frequencies of $p$-Laplace type operators generated by quadratic forms. Optimal constants are exhibited, rigidity of the upper estimate is proved, anisotropic…
We prove a suite of asymptotically sharp quadratic curvature pinching estimates for mean curvature flow in the sphere which generalize Simons' rigidity theorem for minimal hypersurfaces. We then obtain derivative estimates for the second…
The effective stress tensor of a homogeneous turbulent rotating fluid is anisotropic. This leads us to consider the most general axisymmetric four-rank ``viscosity tensor'' for a Newtonian fluid and the new terms in the turbulent effective…
We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at a high temporal frequency, we use limit theorems for multipower variations and…
We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an…
We provide a sharp double-sided estimate for Poincar\'e-Sobolev constants on a convex set, in terms of its inradius and $N-$dimensional measure. Our results extend and unify previous works by Hersch and Protter (for the first eigenvalue)…
Tensorial curvature measures are tensor-valued generalizations of the curvature measures of convex bodies. We prove a complete set of kinematic formulae for such tensorial curvature measures on convex bodies and for their (nonsmooth)…
Recent experimental observation of inertial spin dynamics calls upon holistic reevaluation of the theoretical framework of magnetic resonance in ferromagnets. Here, we derive the secular equation of an inertial spin system in analogy to the…
The underlying motivation of the present work lies on a cornerstone question in spectral optimization that consists of determining sharp lower and upper uniform estimates for fundamental frequencies of a set of uniformly elliptic operators…
We consider a partially hinged rectangular plate and its normal modes. There are two families of modes, longitudinal and torsional. We study the variation of the corresponding eigenvalues under domain deformations. We investigate the…
A brief review is given of recent results devoted to the effects of large-scale anisotropy on the inertial-range statistics of the passive scalar quantity $\theta(t,{\bf x})$, advected by the synthetic turbulent velocity field with the…
In this paper, we first prove monotonicity of a generalized para bolic frequency on weighted closed Riemannian manifolds for some linear heat equation. Secondly, a certain generalized parabolic frequency functional is defined with respect…
We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…
An inequality on torsional rigidity is established. For tangential polygons this inequality is stronger than an inequality of Polya and Szego for convex domains. (A survey of related work, not in the journal submission, is presented in the…
The model for high frequency electrodynamics in anisotropic type-II superconductors in the vortex state is studied considering arbitrary orientations between the applied field, the applied current and the anisotropy axis. An anisotropic…
The N\'eel order of an antiferromagnet subject to a spin torque can undergo precession in a circular orbit about any chosen axis. To orient and stabilize the motion against the effects of magnetic anisotropy, the spin polarization should…