Communications in Mathematical Physics

, Volume 200, Issue 2, pp 421-444

First online:

Harnack Type Inequality: the Method of Moving Planes

  • Yan Yan LiAffiliated withDepartment of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, USA.¶E-mail:

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A Harnack type inequality is established for solutions to some semilinear elliptic equations in dimension two. The result is motivated by our approach to the study of some semilinear elliptic equations on compact Riemannian manifolds, which originated from some Chern–Simons Higgs model and have been studied recently by various authors.