8 papers · 1 filter
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…
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-…
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…