Qualitative properties of a non-linear system involving the p-Laplacian operator and a De Giorgi type result

Abstract

In this article, we consider the non-linear system involving the -Laplacianfor which we prove symmetry, asymptotic behaviour and non-degeneracy properties. Next, we prove a De Giorgi type result in dimension 2 under some additional growth and monotonicity assumptions.

Keywords:

• p-Laplacian
• systems
• De Giorgi type results

AMS Subject Classifications:

• 35 J20
• 35 J 50

Acknowledgments

The author wishes to thank Alberto Farina especially for his precious advises and remarks, Enrico Valdinoci and Mohamed Fazly for having pointed out several papers on the question, Isabeau Birindelli for some informal discussions about section 4, and the anonymous referee for their judicious remarks.