Bonheure, DenisCoelho, Maria Isabel EstevesNYS, Manon2017-11-172017-11-172017-02BONHEURE, Denis; COELHO, Maria Isabel Esteves; NYS, Manon - Heteroclinic solutions of singular quasilinear bistable equations. NODEA - Nonlinear Differential Equations and Applications. ISSN 1021-9722. Vol. 24, N.º 1 (2017), pp. 1-291021-97221420-9004http://hdl.handle.net/10400.21/7539In this note we consider the action functional integral(R x ω) (1-root [1-(|∇u|)^2] + W(u) dx¯), where W is a double well potential and ω is a bounded domain of RN-1. We prove existence, one-dimensionality and uniqueness (up to translations) of a smooth minimizing phase transition between the two stable states u=-1 and u=1. The question of existence of at least one minimal heteroctinic connection for the non-autonomous model integral(R) (1-root [1-(|u’|)^2]+a(t)W(u))dt is also addressed. For this functional, we look for the possible assumptions on a(t) ensuring the existence of a minimizer.engMean curvature operator in Lorentz–Minkowski spaceFree energy functionalPhase transitionIncreasing rearrangementRigiditySymmetryjournal article10.1007/s00030-016-0418-6