2013/09/12 by Francesca Alessio, Piero Montecchiari, Alessio, Francesca G. +1
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1309.3104
openalex publication_date 2013/09/12 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We study the existence of solutions u: R3\→ R2 for the semilinear\nelliptic systems \
labeleq:abs -
Delta u(x,y,z)+
nabla\nW(u(x,y,z))=0, where W: R2\→ R is a double well symmetric\npotential. We use variational methods to show, under generic non degenerate\nproperties of the set of one dimensional heteroclinic connections between the\ntwo minima a\± of W, that ( refeq:abs) has infinitely many\ngeometrically distinct solutions u\∈ C2( R3, R2) which satisfy\nu(x,y,z)\→ a\± as x\→\±\∞ uniformly with respect to\n(y,z)\∈ R2 and which exhibit dihedral symmetries with respect to the\nvariables y and z. We also characterize the asymptotic behaviour of these\nsolutions as |(y,z)|\→ +\∞.\n