IBVP for anisotropic fractional type degenerate parabolic equation

This paper is a generalization of the author’s previous work [14]. We extend the argument [14] for any uniformly elliptic operator in divergence form $\mathcal{L}u=-div(A(x)\mathrm{\nabla }u)$, more precisely, we study a fractional type degenerate elliptic equation posed in bounded domains $${\mathrm{\partial }}_{t}u=div(uA(x)\mathrm{\nabla }{\mathcal{L}}^{-s}u)$$ where ${\mathcal{L}}^{-s}$ is the inverse $s$-fractional elliptic operator for any $s\in (0,1)$. We show the existence of solutions for measurable and bounded non-negative initial data, and homogeneous Dirichlet boundary condition.