Some Remarks on Energy inequalities for harmonic maps with potential
  In this note we discuss how several results characterizing the qualitative behavior of solutions to the nonlinear Poisson equation can be generalized to harmonic maps with potential between complete Riemannian manifolds. This includes gradient estimates, monotonicity formulas and Liouville theorems under curvature and energy assumptions. 
Volker Branding
math.DG math-ph math.AP math.MP