Fractional nonlinear degenerate diffusion equations on bounded domains part I. Existence, uniqueness and upper bounds

We investigate quantitative properties of nonnegative solutions u(t,x)≥0 to the nonlinear fractional diffusion equation, ∂tu+LF(u)=0 posed in a bounded domain, x∈Ω⊂RN, with appropriate homogeneous Dirichlet boundary conditions. As L we can use a quite general class of linear operators that includes the two most common versions of the fractional Laplacian (−Δ)s, 0