Boundedness and contractive estimates for orthotropic, widely degenerate, doubly nonlinear diffusion equations

We study the regularity of weak solutions to doubly nonlinear orthotropic evolution equations of the form \[ \partial_{t}(\vert u\vert^{α-1}u)-\sum_{i=1}^{N}\partial_{i}\left[a_{i}(x,t)\,(|\partial_{i}u|-δ_{i})_{+}^{p-1}\frac{\partial_{i}u}{\vert\partial_{i}u\vert}\right]=f\,\,\,\,\,\,\,\,\,\,\mathr