#### Paper Mentions

#### 612 Citations

Eigenvalue Estimates for $p$-Laplace Problems on Domains Expressed in Fermi Coordinates

- Mathematics
- 2021

We prove explicit and sharp eigenvalue estimates for Neumann p-Laplace eigenvalues in domains that admit a representation in Fermi coordinates. More precisely, if γ denotes a non-closed curve in R… Expand

Sharp Poincar\'e inequalities in a class of non-convex sets

- Mathematics
- 2016

Let $\gamma$ be a smooth curve whose image is symmetric with respect to the y-axis, and let D be a planar domain consisting of the points on one side of $\gamma$, within a suitable distance $\delta$… Expand

On Constants in Maxwell Inequalities for Bounded and Convex Domains

- Mathematics
- 2015

It is shown that for a bounded and convex domain Ω ⊂ ℝ3, the Maxwell constants are bounded from below and above by the Friedrichs and Poincaré constants of Ω, respectively. Bibliography: 14 titles.

Needle decompositions in Riemannian geometry

- Mathematics
- 2014

The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, our method is based on the following… Expand

A Proof of Bobkov's Spectral Bound For Convex Domains via Gaussian Fitting and Free Energy Estimation

- Mathematics, Physics
- 2012

We obtain a new proof of Bobkov's lower bound on the first positive eigenvalue of the (negative) Neumann Laplacian (or equivalently, the Cheeger constant) on a bounded convex domain $K$ in Euclidean… Expand

An optimal Poincare inequality in L^1 for convex domains

- Mathematics
- 2003

For convex domains Ω C R n with diameter d we prove ∥u∥ L 1 (ω) ≤ d 2 ∥⊇ u ∥ L 1 (ω) for any u with zero mean value on w. We also show that the constant 1/2 in this inequality is optimal.

Distributed stabilization of Korteweg-de Vries-Burgers equation in the presence of input delay

- Mathematics, Computer Science
- Autom.
- 2019

A new Lyapunov–Krasovskii functional is suggested that leads to regional stability conditions of the closed-loop system in terms of linear matrix inequalities (LMIs) by solving these LMIs and an upper bound on the delay that preserves regional stability can be found. Expand

Functional Inequalities on Weighted Riemannian Manifolds Subject to Curvature-Dimension Conditions

- Mathematics
- 2019

We establish new sharp inequalities of Poincare or log-Sobolev type, on geodesically-convex weighted Riemannian manifolds $(M,\mathfrak{g},\mu)$ whose (generalized) Ricci curvature… Expand

A SHORT NOTE ON HELMHOLTZ DECOMPOSITIONS FOR BOUNDED DOMAINS IN R

- 2018

In this short note we consider several widely used L-orthogonal Helmholtz decompositions for bounded domains in R. It is well known that one part of the decompositions is a subspace of the space of… Expand

A Short Note on Helmholtz Decompositions for Bounded Domains in $\mathbb{R}^3$.

- Mathematics
- 2018

In this short note we consider several widely used ${\sf L}^2$-orthogonal Helmholtz decompositions for bounded domains in $\mathbb{R}^3$. It is well known that one part of the decompositions is a… Expand

#### References

SHOWING 1-7 OF 7 REFERENCES

New bounds for solutions of second order elliptic partial differential equations

- Mathematics
- 1958

1. Introduction In a previous paper [10] the authors presented methods for determining, with arbitrary and known accuracy, the Dirichlet integral and the value at a point of a solution of Laplace's… Expand

Lower Bounds for Vibration Frequencies of Elastically Supported Membranes and Plates

- Mathematics
- 1957

If R is two-dimensional, the eigenvalues Xi(k) are proportional to the squares of the frequencies of a membrane covering R and elastically supported on the boundary B. If R is three-dimensional they… Expand

Methoden der mathematischen Physik

- Philosophy
- 1924

VIII uber den Inhalt im einzelnen unterrichtet das ausfuhrliche Ver zeichnis. Zur Form ist etwas Grundsatzliches zu sagen: Das klassische Ideal einer gewissermassen atomistischen Auffassung der… Expand