The local boundary estimate of weak solutions to fractional $ p $-Laplace equations

In this paper, we investigate weak solutions to equations of fractional $ p $-Laplace type. We obtain several local boundary estimates about weak solutions in Bessel space by the Lipschitz truncation method and the pointwise Hardy inequality. The estimates are global over bounded domains that satisfy an exterior uniform thickness condition, which involves the fractional $ (s, p) $-capacity.