Transmission problems for the fractional p-Laplacian across fractal interfaces

We consider a parabolic transmission problem, involving nonlinear fractional operators of different order, across a fractal interface sigma. The transmission condition is of Robin type and it involves the jump of the p fractional normal derivatives on the irregular interface. After proving existence and uniqueness results for the weak solution of the problem at hand, via a semigroup approach, we investigate the regularity of the nonlinear fractional semigroup.