# IBVP for anisotropic fractional type degenerate parabolic equation

## TL;DR

This paper generalizes previous work on fractional degenerate parabolic equations, establishing existence results for solutions involving anisotropic fractional operators in bounded domains.

## Contribution

It extends the analysis to any uniformly elliptic divergence form operator and studies a fractional degenerate elliptic equation with new existence results.

## Key findings

- Existence of solutions for measurable, bounded, non-negative initial data.
- Solutions satisfy homogeneous Dirichlet boundary conditions.
- Generalization to any uniformly elliptic operator in divergence form.

## Abstract

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 $\mathcal{L}u=-div(A(x)\nabla u)$, more precisely, we study a fractional type degenerate elliptic equation posed in bounded domains $$ \partial_t u=div(u\,A(x)\nabla \mathcal{L}^{-s}u) $$ 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.