23 citations · 59 across the 19 of their papers we have counts for
20 papers
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^…
A clustering theorem in fractional Sobolev spaces
Fatma Gamza Düzgün, Antonio Iannizzotto, Vincenzo Vespri
We prove a general clustering result for the fractional Sobolev space : whenever the positivity set of a function in a square has measure bounded from below by a multi…
Hölder estimates of weak solutions to degenerate chemotaxis systems with a source term
M. Marras, F. Ragnedda, S. Vernier-Piro +1
In this note we consider degenerate chemotaxis systems with porous media type diffusion and a source term satisfying the Hadamard growth condition. We prove the Hölder regularity f…
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…
A new framework for polynomial approximation to differential equations
Luigi Brugnano, Gianluca Frasca-Caccia, Felice Iavernaro +1
In this paper we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The framework, initially devised for the…
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…
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…
Remarks on Sobolev-Morrey-Campanato spaces defined on domains
Pier Domenico Lamberti, Vincenzo Vespri
We discuss a few old results concerning embedding theorems for Campanato and Sobolev-Morrey spaces adapting the formulations to the case of domains of class , and we prese…
An extensive study of the regularity properties of solutions to doubly singular equations
Vincenzo Vespri, Matias Vestberg
In recent years, many papers have been devoted to the regularity of doubly nonlinear singular evolution equations. Many of the proofs are unnecessarily complicated, rely on superfl…
Anisotropic Sobolev embeddings and the speed of propagation for parabolic equations
F. G. Düzgün, S. Mosconi, V. Vespri
We consider a quasilinear parabolic Cauchy problem with spatial anisotropy of orthotropic type and study the spatial localization of solutions. Assuming the initial datum is locali…
Decay estimates for evolutionary equations with fractional time-diffusion
Serena Dipierro, Enrico Valdinoci, Vincenzo Vespri
We consider an evolution equation whose time-diffusion is of fractional type and we provide decay estimates in time for the -norm of the solutions in a bounded domain. The spa…
Remarks on Local Boundedness and Local Hölder Continuity of Local Weak Solutions to Anisotropic -Laplacian Type Equations
Emmanuele DiBenedetto, Ugo Gianazza, Vincenzo Vespri
Locally bounded, local weak solutions to a special class of quasilinear, anisotropic, -Laplacian type elliptic equations, are shown to be locally Hölder continuous. Homogeneous…
-Dimensional Harnack Estimates
Fatma Gamze Düzgün, Ugo Gianazza, Vincenzo Vespri
Let be a non-negative super-solution to a -dimensional singular parabolic equation of -Laplacian type (). If is bounded below on a time-segment $\{y\}\times(0,…
Symmetry and linear stability in Serrin's overdetermined problem via the stability of the parallel surface problem
Giulio Ciraolo, Rolando Magnanini, Vincenzo Vespri
We consider the solution of the problem $$ -Δu=f(u) \ \mbox{ and } \ u>0 \ \ \mbox{ in } \ Ω, \ \ u=0 \ \mbox{ on } \ Γ, $$ where is a bounded domain in with bou…
Hölder stability for Serrin's overdetermined problem
Giulio Ciraolo, Rolando Magnanini, Vincenzo Vespri
In a bounded domain , we consider a positive solution of the problem in , on , where is a locally Lipschitz continuou…
Continuity in two dimensions for a very degenerate elliptic equation
Filippo Santambrogio, Vincenzo Vespri
An elliptic equation div(F(Du)) = f whose ellipticity strongly degenerates for small values of Du (say, F = 0 on B(0,1)) is considered. The aim is to prove regularity for F(Du). Th…