14 papers
The weak Harnack inequality and the rigidity of the anisotropic Trudinger's equation
Simone Ciani, Mattia Galeotti, Igor Skrypnik
We prove a local weak Harnack inequality for nonnegative weak super-solutions to the anisotropic Trudinger equation. As an application, we show a proof of the Harnack inequality th…
Harnack estimates for the nonlocal Trudinger equation
Simone Ciani, Kenta Nakamura
We carry on a study of the point-wise regularity theory for the nonlocal Trudinger equation, with measurable and bounded singular kernel. We establish refined quantitative upper bo…
Widely degenerate anisotropic diffusion: local boundedness and semicontinuity
Pasquale Ambrosio, Simone Ciani, Giovanni Cupini
We investigate the regularity of local weak solutions to evolution equations of the form \[ \partial_{t}u\,=\,\sum_{i=1}^{n}\,\partial_{x_{i}}\left[a_{i}(x,t)\,(\vert\partial_{x_{i…
Regularity for Doubly Nonlinear Equations in the Mixed Regime
Simone Ciani, Eurica Henriques, Mariia Savchenko +2
We study the local Hölder continuity of nonnegative solutions to doubly nonlinear equations by introducing a new technique that allows us to treat the cases where the equation is b…
Integral Harnack estimates and the rate of extinction of singular fractional diffusion
Filippo M. Cassanello, Simone Ciani, Antonio Iannizzotto
We prove several integral Harnack-type inequalities for local weak solutions of parabolic equations with measurable and bounded coefficients, describing singular s-fractional p-Lap…
Nonlocal parabolic De Giorgi classes
Simone Ciani, Kenta Nakamura
We propose a new paradigm for the point-wise regularity theory of parabolic nonlocal problems, by addressing directly the elements of a wide parabolic energy class. First we carry…
Qualitative properties of solutions to parabolic anisotropic equations: Part I -- Expansion of positivity
Simone Ciani, Eurica Henriques, Mariia Savchenko +1
We prove expansion of positivity and reduction of the oscillation results to the local weak solutions to a doubly nonlinear anisotropic class of parabolic differential equations wi…
Qualitative properties of solutions to parabolic anisotropic equations: Part II. The anisotropic Trudinger's equation
Simone Ciani, Eurica Henriques, Mariia O. Savchenko +1
We study the local regularity properties of weak solutions to a special class of anisotropic doubly nonlinear parabolic operators, whose prototype is the anisotropic Trudinger's eq…
Parabolic De Giorgi classes with doubly nonlinear, nonstandard growth: local boundedness under exact integrability assumptions
Simone Ciani, Eurica Henriques, Mariia O. Savchenko +1
We define a suitable class of functions bearing unbalanced energy estimates, that are embodied by local weak subsolutions to doubly nonlinear, double-phase, Orlicz-…
Phragmén-Lindelöf-type theorems for functions in Homogeneous De Giorgi Classes
Simone Ciani, Ugo Gianazza, Zheng Li
We study Phragmén-Lindelöf-type theorems for functions in homogeneous De Giorgi classes, and we show that the maximum modulus of has a power-like growth of order $…
The weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth
Simone Ciani, Eurica Henriques, Igor i. Skrypnik
In this work we prove that the non-negative functions , for some , belonging to the De Giorgi classes \begin{equation}\label{eq0.1} \fint\limits_{B_{r(1-σ)…
Fine boundary continuity for degenerate double-phase diffusion
Simone Ciani, Eurica Henriques, Igor Skrypnik
We study the boundary behavior of solutions to parabolic double-phase equations through the celebrated Wiener's sufficiency criterion. The analysis is conducted for cylindrical dom…
Harnack-type estimates and extinction in finite time for a class of anisotropic porous medium type equations
Eurica Henriques, Simone Ciani
In this work we are interested in the study of a class of anisotropic porous medium-type equations whose prototype is \[ u_t =\sum_{i=1}^N \left( m_i u^{m_i-1} u_{x_i} \right)_{x_i…
The impact of intrinsic scaling on the rate of extinction for anisotropic non-Newtonian fast diffusion
Simone Ciani, Eurica Henriques, Igor Skrypnik
We study the decay towards the extinction that pertains to local weak solutions to fully anisotropic equations whose prototype is \[ \partial_t u= \sum_{i=1}^N \partial_i (|\partia…