Elliptic differential inequalities with applications to harmonic maps (Q1309194)

The authors begin with a detailed study of an ordinary differential equation on \(\mathbb{R}\) of the form \(\alpha'' (t) + g(t) \alpha' (t) = f(\alpha (t))\). That is applied (1) to obtain apriori estimates for the energy density of bounded harmonic maps \(\varphi : M \to N\), where the Ricci curvature of \(M\) has growth at \(\infty\), and \(N\) has nonpositive sectional curvature; (2) to problems involving suitable rotational symmetry. Proper attention is paid to various interactions with related literature, both old and new.