2 citations · 2 across the 4 of their papers we have counts for
5 papers · 1 filter
Geometric aspects of the Harnack Inequality for a nonlocal heat equation
Mateusz Dembny, Mikołaj Sierżęga
We establish a connection between a sharp double-sided Harnack bound for positive solutions of a fractional heat equation and the circular geometry in higher dimensions. The presen…
A sharp Harnack bound for a nonlocal heat equation
Mateusz Dembny, Mikołaj Sierżęga
A sharp double-sided Harnack bound is derived for positive solutions of a fractional order heat equation.
Optimal Liouville theorem for a semilinear Ornstein-Uhlenbeck equation
Michał Fabisiak, Mikołaj Sierżęga
The question of triviality of solutions of the semilinear Ornstein-Uhlenbeck equation, \[ Δw-\frac{1}{2} \langle x,\nabla w\rangle-\fracλ{p-1}w+|w|^{p-1}w=0, \] is considered. It i…
Existence and nonexistence of solutions to the Hardy parabolic equation
Kotaro Hisa, Mikołaj Sierżęga
In this paper, we obtain necessary conditions and sufficient conditions on the initial data for the local-in-time solvability of the Cauchy problem \[ \partial_t u +(-Δ)^\fracθ{2}…
A note on well-posedness of semilinear reaction-diffusion problem with singular initial data
James C. Robinson, Mikołaj Sierżęga
We discuss conditions for well-posedness of the scalar reaction-diffusion equation equipped with Dirichlet boundary conditions where the initial data is unbounded.…