Now showing items 1-4 of 4

• #### A comparison principle for vector valued minimizers of semilinear elliptic energy, with application to dead cores ﻿

(2021)
We establish a comparison principle providing accurate upper bounds for the modulus of vector valued minimizers of an energy functional, associated when the potential is smooth, to elliptic gradient systems. Our assumptions ...
• #### Double layered solutions to the extended Fisher–Kolmogorov P.D.E. ﻿

(2021-06-22)
We construct double layered solutions to the extended Fisher–Kolmogorov P.D.E., under the assumption that the set of minimal heteroclinics of the corresponding O.D.E. satisfies a separation condition. The aim of our work ...
• #### Entire vortex solutions of negative degree for the anisotropic Ginzburg-Landau system ﻿

(2022)
The anisotropic Ginzburg-Landau system $\Delta u+\delta \nabla (div u) +\delta curl^*(curl u)=(|u|^2-1) u$, for $u\colon\mathbb R^2\to\mathbb R^2$ and $\delta\in (-1,1)$, models the formation of vortices in liquid crystals. ...
• #### Nondegeneracy of heteroclinic orbits for a class of potentials on the plane ﻿

(2021)
In the scalar case, the nondegeneracy of heteroclinic orbits is a well-known property, commonly used in problems involving nonlinear elliptic, parabolic or hyperbolic P.D.E. On the other hand, Schatzman proved that in the ...