23 research outputs found
The fractional Hardy inequality with a remainder term
We calculate the regional fractional Laplacian on some power function on an
interval. As an application, we prove Hardy inequality with an extra term for
the fractional Laplacian on the interval with the optimal constant. As a
result, we obtain the fractional Hardy inequality with best constant and an
extra lower-order term for general domains, following the method developed by
M. Loss and C. Sloane [arXiv:0907.3054v1 [math.AP]]Comment: Major change
Hardy inequalities and non-explosion results for semigroups
We prove non-explosion results for Schr\"odinger perturbations of symmetric
transition densities and Hardy inequalities for their quadratic forms by using
explicit supermedian functions of their semigroups.Comment: 21 pages, updated reference
Comparability and regularity estimates for symmetric nonlocal Dirichlet forms
The aim of this work is to study comparability of nonlocal Dirichlet forms.
We provide sufficient conditions on the kernel for local and global
comparability. As an application we prove a-priori estimates in H\"{o}lder
spaces for solutions to integrodifferential equations. These solutions are
defined with the help of symmetric nonlocal Dirichlet forms.Comment: 17 pages, 1 figur