23 citations · 28 across the 13 of their papers we have counts for
14 papers
Local boundedness for weak solutions to strongly degenerate orthotropic parabolic equations
Pasquale Ambrosio, Simone Ciani
We prove the local boundedness of local weak solutions to the parabolic equation \[ \partial_{t}u\,=\,\sum_{i=1}^{n}\partial_{x_{i}}\left[(\vert u_{x_{i}}\vert-δ_{i})_{+}^{p-1}\fra…
Gaussian estimates vs. elliptic regularity on open sets
Tim Böhnlein, Simone Ciani, Moritz Egert
Given an elliptic operator subject to mixed boundary conditions on an open subset of , we study the relation between Gaussian poi…
Boundedness, Ultracontractive Bounds and Optimal Evolution of the Support for Doubly Nonlinear Anisotropic Diffusion
Simone Ciani, Vincenzo Vespri, Matias Vestberg
We investigate some regularity properties of a class of doubly nonlinear anisotropic evolution equations whose model case is \begin{align*} \partial_t \big(|u|^{α-1}u \big) - \sum^…
Liouville rigidity and time-extrinsic Harnack estimates for an anisotropic slow diffusion
Simone Ciani, Umberto Guarnotta
We prove that ancient non-negative solutions to a fully anisotropic prototype evolution equation are constant if they satisfy a condition of finite speed of propagation and if they…
A note on the point-wise behaviour of bounded solutions for a non-standard elliptic operator
Laura Baldelli, Simone Ciani, Igor I. Skrypnik +1
In this brief note we discuss local Hölder continuity for solutions to anisotropic elliptic equations of the type $ \sum_{i=1}^s \partial_{ii} u+ \sum_{i=s+1}^N \partial_i \bigg(A_…
On a particular scaling for the prototype anisotropic p-Laplacian
Simone Ciani, Umberto Guarnotta, Vincenzo Vespri
In this brief note we show that under a volume non-preserving scaling it is possible to recover the basics for a regularity theory regarding local weak solutions to a parabolic ful…