10 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…
On the Hölder continuity of signed solutions to doubly nonlinear parabolic equations in the mixed degenerate/singular cases
Igor I. Skrypnik
We prove the Hölder continuity of sign-changing solutions to the equation of the type where n…
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-…
On the continuity of solutions to the anisotropic -Laplacian with lower order term
Mariia Savchenko, Igor Skrypnik, Yevgeniia Yevgenieva
We establish the continuity of bounded solutions to the anisotropic elliptic equation $$-\sum\limits_{i=1}^N\Big(|u_{x_i}|^{p_i-2} u_{x_i}\Big)_{x_i}=f(x),\quad x\in Ω,\quad f(x)\i…
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…
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…