48 citations · 194 across the 35 of their papers we have counts for
8 papers · 2 filters
On the existence of dark solitons of the cubic nonlinear Schrodinger equation with periodic inhomogeneous nonlinearity
Christos Sourdis
We provide a simple proof of the existence of dark solitons of the defocusing cubic nonlinear Schrodinger equation with periodic inhomogeneous nonlinearity. Moreover, our proof all…
On the growth of the energy of entire solutions to the vector Allen-Cahn equation
Christos Sourdis
We prove that the energy over balls of entire, nonconstant, bounded solutions to the vector Allen-Cahn equation grows faster than , for any , as the volume…
Energy estimates for minimizers to a class of elliptic systems of Allen-Cahn type and the Liouville property
Christos Sourdis
We prove a theorem for the growth of the energy of bounded, globally minimizing solutions to a class of semilinear elliptic systems of the form , $x\in \mathbb{R}^n…
On a maximum principle for vector minimizers to the Allen-Cahn energy
Christos Sourdis
By using the unique continuation principle for linear elliptic systems, we can simplify the proof of a recent variational maximum principle due to Alikakos and Fusco. At the same t…
A new monotonicity formula for solutions to the elliptic system
Christos Sourdis
Using a physically motivated stress energy tensor, we prove weak and strong monotonicity formulas for solutions to the semilinear elliptic system with nonnegat…
A Liouville theorem for minimizers with finite potential energy for the vectorial Allen-Cahn equation
Christos Sourdis
We prove that if a globally minimizing solution to the vectorial Allen-Cahn equation has finite potential energy, then it is a constant.