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Publications Influence

On De Giorgi's conjecture in dimension N>9

- M. Pino, M. Kowalczyk, J. Wei
- Mathematics
- 1 November 2011

A celebrated conjecture due to De Giorgi states that any bounded solution of the equation u + (1 u 2 )u = 0 in R N with @yNu > 0 must be such that its level setsfu = g are all hyperplanes, at least… Expand

202 15

Concentration on curves for nonlinear Schrödinger Equations

- M. A. Pino, M. Kowalczyk, J. Wei
- Mathematics
- 2007

We consider the problem
where p > 1, e > 0 is a small parameter, and V is a uniformly positive, smooth potential. Let Γ be a closed curve, nondegenerate geodesic relative to the… Expand

148 10- PDF

Variational reduction for Ginzburg–Landau vortices

- M. A. Pino, M. Kowalczyk, Monica Musso
- Mathematics
- 15 October 2006

Let Ω be a bounded domain with smooth boundary in R2. We construct non-constant solutions to the complex-valued Ginzburg–Landau equation e2Δu+(1−|u|2)u=0 in Ω, as e→0, both under zero Neumann and… Expand

34 7- PDF

MULTIPLE-END SOLUTIONS TO THE ALLEN-CAHN EQUATION IN R2

- M. Pino, M. Kowalczyk, F. Pacard, J. Wei
- Mathematics
- 15 January 2010

We construct a new class of entire solutions for the Allen–Cahn equation Δu+(1−u2)u=0, in R2(∼C). Given k⩾1, we find a family of solutions whose zero level sets are, away from a compact set,… Expand

78 3- PDF

Moduli space theory for the allen-cahn equation in the plane

- M. Pino, M. Kowalczyk, F. Pacard
- Mathematics
- 9 August 2012

In this paper we study entire solutions of the Allen-Cahn equation \Delta u - F'(u) = 0, where F is an even, bistable function. We are particularly interested in the description of the moduli space… Expand

32 3- PDF

Interface Foliation near Minimal Submanifolds in Riemannian Manifolds with Positive Ricci Curvature

- M. Pino, M. Kowalczyk, J. Wei, J. Yang
- Mathematics
- 17 June 2010

Let $${(\mathcal {M},\tilde{g})}$$ be an N-dimensional smooth compact Riemannian manifold. We consider the singularly perturbed Allen–Cahn equation$$\varepsilon ^2 \Delta _{\tilde g} u \, + \, (1 -… Expand

45 3- PDF

Traveling Waves with Multiple and Nonconvex Fronts for a Bistable Semilinear Parabolic Equation

- M. Pino, M. Kowalczyk, J. Wei
- Mathematics
- 1 April 2013

We construct new examples of traveling wave solutions to the bistable and balanced semilinear parabolic equation in \input amssym ${\Bbb R}^N+1$, . Our first example is that of a traveling wave… Expand

22 2- PDF

Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation

- M. Clerc, J. Dávila, M. Kowalczyk, Panayotis Smyrnelis, E. Vidal-Henriquez
- Mathematics
- 10 October 2016

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 the parameters… Expand

15 2- PDF

A counterexample to a conjecture by De Giorgi in large dimensions

- M. A. Pino, M. Kowalczyk, J. Wei
- Mathematics
- 1 December 2008

We consider the Allen–Cahn equation
Δu+u(1−u2)=0in RN.
A celebrated conjecture by E. De Giorgi (1978) states that if u is a bounded solution to this problem such that ∂xNu>0, then the level sets… Expand

31 2- PDF

Nondegeneracy of the saddle solution of the Allen-Cahn equation

- M. Kowalczyk, Yianghao Liu
- Mathematics
- 1 December 2011

A solution of the Allen-Cahn equation in the plane is called a saddle solution if its nodal set coincides with the coordinate axes. Such solutions are known to exist for a large class of… Expand

24 1- PDF