5 papers · 2 filters
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…