Nonlocal filtration equations with rough kernels

Arturo de Pablo, Fernando Quirós, Ana Rodríguez

We study the nonlinear and nonlocal Cauchy problem \[ \partial_{t}u+\mathcal{L}φ(u)=0 \quad\text{in }\mathbb{R}^{N}\times\mathbb{R}_+,\qquad u(\cdot,0)=u_0, \] where $\mathcal{L}$…