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.
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}, pages = {149--157}, publisher = {Elsevier}, volume = {28}, number = {2}, year = {2011}, doi = {10.1016/j.anihpc.2011.02.001}, mrnumber = {2784067}, zbl = {1213.35409}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2011.02.001/} }
TY - JOUR AU - Coffman, Adam AU - Pan, Yifei TI - Some nonlinear differential inequalities and an application to Hölder continuous almost complex structures JO - Annales de l'I.H.P. Analyse non linéaire PY - 2011 SP - 149 EP - 157 VL - 28 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2011.02.001/ DO - 10.1016/j.anihpc.2011.02.001 LA - en ID - AIHPC_2011__28_2_149_0 ER -
%0 Journal Article %A Coffman, Adam %A Pan, Yifei %T Some nonlinear differential inequalities and an application to Hölder continuous almost complex structures %J Annales de l'I.H.P. Analyse non linéaire %D 2011 %P 149-157 %V 28 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2011.02.001/ %R 10.1016/j.anihpc.2011.02.001 %G en %F 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/articles/10.1016/j.anihpc.2011.02.001/
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