23 citations · 28 across the 13 of their papers we have counts for
14 papers · 1 filter
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…
On the Local Behavior of Local Weak Solutions to some Singular Anisotropic Elliptic Equations
Simone Ciani, Igor I. Skrypnik, Vincenzo Vespri
We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations that involves both non-degenerate and singular operators. Throughout a para…
Evolution equations with nonlocal initial conditions and superlinear growth
Irene Benedetti, Simone Ciani
We carry out an analysis of the existence of solutions for a class of nonlinear partial differential equations of parabolic type. The equation is associated to a nonlocal initial c…
An Introduction to Barenblatt Solutions for Anisotropic -Laplace Equations
Simone Ciani, Vincenzo Vespri
We introduce Fundamental solutions of Barenblatt type for the equation , , on $Σ_T=\ma…
On Holder Continuity and Equivalent Formulation of Intrinsic Harnack Estimates for an Anisotropic Parabolic Degenerate Prototype Equation
Simone Ciani, Vincenzo Vespri
We give a proof of Hölder continuity for bounded local weak solutions to the equation , in , with $Ω\subset \sub…
Parabolic Harnack estimates for anisotropic slow diffusion
Simone Ciani, Sunra Mosconi, Vincenzo Vespri
We prove a Harnack inequality for positive solutions of a parabolic equation with slow anisotropic spatial diffusion. After identifying its natural scalings, we reduce the problem…
Dimensional lower bounds for contact surfaces of Cheeger sets
Marco Caroccia, Simone Ciani
We carry on an analysis of the size of the contact surface of a Cheeger set with the boundary of its ambient space . We show that this size is strongly related to the regula…
Existence of Positive Eigenfunctions to an Anisotropic Elliptic Operator via Sub-Super Solutions Method
Simone Ciani, Giovany M. Figueiredo, Antonio Suàrez
Using the sub-supersolution method we study the existence of positive solutions for the anisotropic problem \begin{equation} -\sum_{i=1}^N\frac{\partial}{\partial x_i}\left( \left|…
A new short proof of regularity for local weak solutions for a certain class of singular parabolic equations
Simone Ciani, Vincenzo Vespri
We shall establish the interior Hölder continuity for locally bounded weak solutions to a class of parabolic singular equations whose prototypes are \begin{equation} u_t= \nabla \c…