5 papers · 1 filter
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 $…