9 citations · 20 across the 17 of their papers we have counts for
22 papers
Energy minimizers in a periodic phase transition model of light-matter interaction in nematic liquid crystals
Panayotis Smyrnelis, Marcel G. Clerc, Manuel Diaz-Zuniga +1
In this paper we complete the study of global minimizers of a forced, non autonomous, one dimensional, phase transition model, initiated in [8]. Motivated by the recent findings in…
Biharmonic nonlinear vector field equations in
Ioannis Arkoudis, Panayotis Smyrnelis
Following the approach of Brezis and Lieb, we prove the existence of a ground state solution for the biharmonic nonlinear vector field equations in the limiting case of space dimen…
Ground state of some variational problems in Hilbert spaces and applications to P.D.E
Ioannis Arkoudis, Panayotis Smyrnelis
We prove the existence of a ground state for some variational problems in Hilbert spaces, following the approach of Berestycki and Lions. Next, we examine the problem of constructi…
Some one-dimensional elliptic problems with constraints
Jacopo Schino, Panayotis Smyrnelis
Given and , we find solutions to the problem \begin{equation*} \begin{cases} \bigl(-\frac{\mathrm{d}^2}{\mathrm{d} x^2}\bigr)^m u +…
Binormal measures
Emmanuel P. Smyrnelis, Panayotis Smyrnelis
Our starting point is the measure , where is the harmonic measure relative to and are…
Some rigidity results and asymptotic porperties for solutions to semilinear elliptic P.D.E
Matteo Rizzi, Panayotis Smyrnelis
We will present some rigidity results for solutions to semilinear elliptic equations of the form $\Deltau = W'(u)$, where W is a quite general potential with a local minimum and a…
Entire vortex solutions of negative degree for the anisotropic Ginzburg-Landau system
Michał Kowalczyk, Xavier Lamy, Panayotis Smyrnelis
The anisotropic Ginzburg-Landau system \[ Δu+δ\, \nabla (\mathrm{div}\: u) +δ\, \mathrm{curl}^*(\mathrm{curl}\: u)=(|u|^2-1) u, \] for and $δ\in…
Nondegeneracy of heteroclinic orbits for a class of potentials on the plane
Jacek Jendrej, Panayotis Smyrnelis
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…
A comparison principle for vector valued minimizers of semilinear elliptic energy, with application to dead cores
Panayotis Smyrnelis
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…
Double layered solutions to the extended Fisher-Kolmogorov P.D.E.
Panayotis Smyrnelis
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 s…
Vortex solutions in the Ginzburg-Landau-Painlevé theory of phase transition
Panayotis Smyrnelis
The extended Painlevé P.D.E. system , , , is obtained by multiplying by the linear t…
Connecting orbits in Hilbert spaces and applications to P.D.E
Panayotis Smyrnelis
We prove a general theorem on the existence of heteroclinic orbits in Hilbert spaces, and present a method to reduce the solutions of some P.D.E. problems to such orbits. In our fi…
Blowing up solutions of semilinear P.D.E. with convex potentials
Panayotis Smyrnelis
We consider convex potentials vanishing at and growing sufficiently fast at . Given any open set with Lipschitz and compact bound…
Gradient theory of domain walls in thin, nematic liquid crystals films
Marcel G. Clerc, Michal Kowalczyk, Panayotis Smyrnelis
In this paper we describe domain walls appearing in a thin, nematic liquid crystal sample subject to an external field with intensity close to the Fréedericksz transition threshold…
The connecting solution of the Painlevé phase transition model
Marcel G. Clerc, Michał Kowalczyk, Panayotis Smyrnelis
The second Painlevé O.D.E. , is known to play an important role in the theory of integrable systems, random matrices, Bose-Einstein condensates an…
Minimal heteroclinics for a class of fourth order O.D.E. systems
Panayotis Smyrnelis
We prove the existence of minimal heteroclinic orbits for a class of fourth order O.D.E. systems with variational structure. In our general set-up, the set of equilibria of these s…
Symmetry breaking and restoration in the Ginzburg-Landau model of nematic liquid crystals
Marcel Clerc, Michał Kowalczyk, Panayotis Smyrnelis
In this paper we study qualitative properties of global minimizers of the Ginzburg-Landau energy which describes light-matter interaction in the theory of nematic liquid crystals n…
On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations
Li Chen, Panayotis Smyrnelis, Israel Michael Sigal
We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations of superconductivity, with multiple magnetic flux quanta per a fundamental cell. We also r…
Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation
Marcel Clerc, Juan Dávila, Michał Kowalczyk +2
We study global minimizers of an energy functional arising as a thin sample limit in the theory of light-matter interaction in nematic liquid crystals. We show that depending on th…
Multyphase solutions to the vector Allen-Cahn equation: Crystalline and other complex symmetric structures
Peter W. Bates, Giorgio Fusco, Panayotis Smyrnelis
We present a systematic study of entire symmetric solutions of the vector Allen-Cahn equation , where is smooth,…
Gradient estimates for semilinear elliptic systems and other related results
Panayotis Smyrnelis
A periodic connection is constructed for a double well potential defined in the plane. This solution violates Modica's estimate as well as the corresponding Liouville Theorem for g…
On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations
T. Tzaneteas, I. M. Sigal
Building on earlier work, we have given in our paper in Contemporary Mathematics 535, 195-213, 2011 (referred here as [TS]) a proof of existence of Abrikosov vortex lattices in the…