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 α, we construct a manifold with an α-Hölder continuous almost complex structure where the Kobayashi–Royden pseudonorm is not upper semicontinuous.
@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}, volume = {28}, year = {2011}, pages = {149-157}, doi = {10.1016/j.anihpc.2011.02.001}, mrnumber = {2784067}, zbl = {1213.35409}, language = {en}, url = {http://dml.mathdoc.fr/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, Tome 28 (2011) pp. 149-157. doi : 10.1016/j.anihpc.2011.02.001. http://gdmltest.u-ga.fr/item/AIHPC_2011__28_2_149_0/
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