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This paper is a generalization of the author's previous work [14]. We extendthe argument [14] for any uniformly elliptic operator in divergence form$\mathcal{L}u=-div(A(x)\nabla u)$, more precisely, we study a fractional typedegenerate elliptic equation posed in bounded domains $$ \partial_tu=div(u\,A(x)\nabla \mathcal{L}^{-s}u) $$ where $\mathcal{L}^{-s}$ is theinverse $s$-fractional elliptic operator for any $s \in (0,1)$. We show theexistence of solutions for measurable and bounded non-negative initial data,and homogeneous Dirichlet boundary condition.

IBVP for anisotropic fractional type degenerate parabolic equation