Do you want to publish a course? Click here

A strong form of the quantitative Wulff inequality

295   0   0.0 ( 0 )
 Added by Robin Neumayer
 Publication date 2015
  fields
and research's language is English




Ask ChatGPT about the research

Quantitative isoperimetric inequalities for anisotropic surface energies are shown where the isoperimetric deficit controls both the Fraenkel asymmetry and a measure of the oscillation of the boundary with respect to the boundary of the corresponding Wulff shape.

rate research

Read More

93 - Robin Neumayer 2019
In this note, we establish a strong form of the quantitive Sobolev inequality in Euclidean space for $p in (1,n)$. Given any function $u in dot W^{1,p}(mathbb{R}^n)$, the gap in the Sobolev inequality controls $| abla u - abla v|_{p}$, where $v$ is an extremal function for the Sobolev inequality.
The aim of this work is to show a non-sharp quantitative stability version of the fractional isocapacitary inequality. In particular, we provide a lower bound for the isocapacitary deficit in terms of the Fraenkel asymmetry. In addition, we provide the asymptotic behaviour of the $s$-fractional capacity when $s$ goes to $1$ and the stability of our estimate with respect to the parameter $s$.
In the context of driven diffusive systems, for thermodynamic transformations over a large but finite time window, we derive an expansion of the energy balance. In particular, we characterize the transformations which minimize the energy dissipation and describe the optimal correction to the quasi-static limit. Surprisingly, in the case of transformations between homogeneous equilibrium states of an ideal gas, the optimal transformation is a sequence of inhomogeneous equilibrium states.
In this paper we prove a quantitative form of the strong unique continuation property for the Lame system when the Lame coefficients $mu$ is Lipschitz and $lambda$ is essentially bounded in dimension $nge 2$. This result is an improvement of our earlier result cite{lin5} in which both $mu$ and $lambda$ were assumed to be Lipschitz.
We give a short proof of a recently established Hardy-type inequality due to Keller, Pinchover, and Pogorzelski together with its optimality. Moreover, we identify the remainder term which makes it into an identity.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا