We consider some second order quasilinear partial differential inequalities for real-valued functions on the unit ball and find conditions under which there is a lower bound for the supremum of nonnegative solutions that do not vanish at the origin. As a consequence, for complex-valued functions satisfying , , and , there is also a lower bound for on the unit disk. For each , we construct a manifold with an -Hölder continuous almost complex structure where the Kobayashi–Royden pseudonorm is not upper semicontinuous.
Cite this article
Adam Coffman, Yifei Pan, Some nonlinear differential inequalities and an application to Hölder continuous almost complex structures. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 2, pp. 149–157DOI 10.1016/J.ANIHPC.2011.02.001