no. 2
Some nonlinear differential inequalities and an application to Hölder continuous almost complex structures
Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 2, pp. 149-157.

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 f(z) satisfying ∂f/∂z ¯=|f| α , 0<α<1, and f(0)≠0, there is also a lower bound for sup |f| on the unit disk. For each α, we construct a manifold with an α-Hölder continuous almost complex structure where the Kobayashi–Royden pseudonorm is not upper semicontinuous.

DOI : 10.1016/j.anihpc.2011.02.001
Classification : 35R45, 32F45, 32Q60, 32Q65, 35B05
Mots clés : Differential inequality, Almost complex manifold 
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     title = {Some nonlinear differential inequalities and an application to {H\"older} continuous almost complex structures},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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     publisher = {Elsevier},
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Coffman, Adam; Pan, Yifei. Some nonlinear differential inequalities and an application to Hölder continuous almost complex structures. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 2, pp. 149-157. doi : 10.1016/j.anihpc.2011.02.001. http://www.numdam.org/articles/10.1016/j.anihpc.2011.02.001/

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