We consider a family of integral operators which appears when analyzing layered equilibria and front dynamics of a phase kinetics equation with a conservation law. We study the spectra of these operators in $L^2$ and derive a lower bound for the associated quadratic forms in terms of the $H^{-1}$ norm.
The $L^p$-dissipativity of certain differential and integral operators
Nonlocal Poincaré Inequalities for Integral Operators with Integrable Nonhomogeneous Kernels
Estimation of the continuity constants for Bogovskiĭ and regularized Poincaré integral operators
![QR code for arXiv:1411.6896 [math.AP]](http://oss.arxitics.com/images/favicon.svg)