Some nonlinear differential inequalities and an application to Hölder continuous almost complex structures
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 2, p. 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 : https://doi.org/10.1016/j.anihpc.2011.02.001
Classification:  35R45,  32F45,  32Q60,  32Q65,  35B05
Keywords: Differential inequality, Almost complex manifold
@article{AIHPC_2011__28_2_149_0,
     author = {Coffman, Adam and Pan, Yifei},
     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},
     publisher = {Elsevier},
     volume = {28},
     number = {2},
     year = {2011},
     pages = {149-157},
     doi = {10.1016/j.anihpc.2011.02.001},
     zbl = {1213.35409},
     mrnumber = {2784067},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2011__28_2_149_0}
}
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, Volume 28 (2011) no. 2, pp. 149-157. doi : 10.1016/j.anihpc.2011.02.001. http://www.numdam.org/item/AIHPC_2011__28_2_149_0/

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