A logarithmic Sobolev trace inequality is derived. Bounds on the best constant for this inequality from above and below are investigated using the sharp Sobolev inequality and the sharp logarithmic Sobolev inequality. Logarithmic Sobolev inequalities capture the spirit of classical Sobolev inequalities with the logarithm function replacing powers, and they can be considered as limiting cases of...

In this paper, we study the degenerate parabolic variational inequality problem in a bounded domain. First, the weak solutions of the variational inequality are defined. Second, the existence and uniqueness of the solutions in the weak sense are proved by using the penalty method and the reduction method.

The classic Poincaré inequality bounds the Lq-norm of a function f in a bounded domain Ω ⊂ Rn in terms of some Lp-norm of its gradient in Ω. We generalize this in two ways: In the first generalization we remove a set Γ from Ω and concentrate our attention on Λ = Ω \ Γ. This new domain might not even be connected and hence no Poincaré inequality can generally hold for it, or if it does hold it m...

The purpose of this paper is to present a rather simple proof of an inequality of Nečas [9] which is equivalent to the inf-sup condition. This inequality is fundamental in the study of the Stokes equations. The boundary of the domain is only assumed to be Lipschitz.

In this paper, we study the exact controllability and stabilization of a system two wave equations coupled by velocities with an internal, local control acting on only one equation. We distinguish cases. first one, when waves propagate at same speed: using frequency domain approach combined multiplier technique, prove that is exponentially stable coupling region satisfies geometric condition GC...

OBJECTIVE Reduction of socioeconomic inequality in health requires appropriate evidence on health and its distribution based on socioeconomic indicators. The objective of this study was to assess socioeconomic inequality in various health domains and self-rated health (SRH). METHODS This study was conducted using data collected in a survey in 2014 on a random sample of individuals aged 18 and...

to date, a number of numerical methods, including the popular finite-difference time domain (fdtd) technique, have been proposed to simulate ground-penetrating radar (gpr) responses. despite having a number of advantages, the finite-difference method also has pitfalls such as being very time consuming in simulating the most common case of media with high dielectric permittivity, causing the for...

Frequency-domain unsteady lifting-line theory is better developed than its time-domain counterpart. To take advantage of this, this paper transforms kinematics to the frequency domain, performs a convolution and then returns results back time-domain. It demonstrates how well-developed frequency-domain methods can be easily applied problems, enabling prediction forces moments on finite wings und...