28 citations · 60 across the 15 of their papers we have counts for
5 papers · 1 filter
Fractal solutions of linear and nonlinear dispersive partial differential equations
V. Chousionis, M. Burak Erdoğan, Nikolaos Tzirakis
In this paper we study fractal solutions of linear and nonlinear dispersive PDE on the torus. In the first part we answer some open questions on the fractal solutions of linear Sch…
Removable sets for Lipschitz harmonic functions on Carnot groups
Vasilis Chousionis, Valentino Magnani, Jeremy T. Tyson
Let G be a Carnot group with homogeneous dimension Q larger than 2 and let L be a sub-Laplacian on G. We prove that the critical dimension for removable sets of Lipschitz L-harmoni…
Removable sets for homogeneous linear PDE in Carnot groups
Vasilis Chousionis, Jeremy T. Tyson
Let $\cL$ be a homogeneous left invariant differential operator on a Carnot group. Assume that both $\cL$ and $\cL^t$ are hypoelliptic. We study the removable sets for $\cL$-soluti…
Singular integrals on self-similar sets and removability for Lipschitz harmonic functions in Heisenberg groups
Vasilis Chousionis, Pertti Mattila
In this paper we study singular integrals on small (that is, measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind…
Singular integrals on Ahlfors-David regular subsets of the Heisenberg group
Vasilis Chousionis, Pertti Mattila
We investigate certain singular integral operators with Riesz-type kernels on s-dimensional Ahlfors-David regular subsets of Heisenberg groups. We show that -boundedness, and…