Some monotonicity results for general systems of nonlinear elliptic PDEs

Julien Brasseur (1) , Serena Dipierro (2)

1 I2M - Institut de Mathématiques de Marseille
2 Institut für Analysis und Numerik

In this paper we show that minima and stable solutions of a general energy functional of the form integral(Omega) F(del u,del v, u, v, x)dx enjoy some monotonicity properties, under an assumption on the growth at infinity of the energy. Our results are quite general, and comprise some rigidity results which are known in the literature.

Mots clés: monotonicity results; stable solutions; domain perturbations

Domaines: Equations aux dérivées partielles [math.AP]

Julien Brasseur, Serena Dipierro. Some monotonicity results for general systems of nonlinear elliptic PDEs. Journal of Differential Equations, 2016, 261 (5), pp.2854 - 2880. ⟨10.1016/j.jde.2016.05.017⟩. ⟨hal-01486726⟩