SEMI-LINEAR SUB-ELLIPTIC EQUATIONS ON THE HEISENBERG GROUP WITH A SINGULAR POTENTIAL

Houda Mokrani (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

In this work, we study the Dirichlet problem for a class of semi-linear subelliptic equations on the Heisenberg group with a singular potential. The singularity is controlled by Hardy's inequality, and the nonlinearity is controlled by Sobolev's inequality. We prove the existence of a nontrivial solution for a homogenous Dirichlet problem.

Mots clés: Heisenberg group; Hardy's inequality; Sobolev's inequality; Singular potential

Domaines: Equations aux dérivées partielles [math.AP]

Houda Mokrani. SEMI-LINEAR SUB-ELLIPTIC EQUATIONS ON THE HEISENBERG GROUP WITH A SINGULAR POTENTIAL. Communications on Pure and Applied Mathematics, 2009, 8 (5), pp.1619 - 1636. ⟨10.3934/cpaa.2009.8.1⟩. ⟨hal-00315641⟩