5 papers · 1 filter
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…
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…
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 $…