TY - JOUR
T1 - Maximum principle for Pucci equations with sublinear growth in Du and its applications
AU - Koike, Shigeaki
AU - Kosugi, Takahiro
N1 - Funding Information:
S. Koike is supported by Grant-in-Aid for Scientific Research (No. 23340028) of JSPS. T. Kosugi is supported by Grant-in-Aid for JSPS Research Fellow 16J01494.
Publisher Copyright:
© 2017 Elsevier Ltd
PY - 2017/9
Y1 - 2017/9
N2 - It is obtained that there exist strong solutions of Pucci extremal equations with sublinear growth in Du and measurable ingredients. It is proved that a strong maximum principle holds in a local sense in Lemma 4.1 although even the (weak) maximum principle fails. By using this existence result, it is shown that the ABP type maximum principle and the weak Harnack inequality for viscosity solutions hold true. As an application, the Hölder continuity for viscosity solutions of possibly singular, quasilinear equations is established.
AB - It is obtained that there exist strong solutions of Pucci extremal equations with sublinear growth in Du and measurable ingredients. It is proved that a strong maximum principle holds in a local sense in Lemma 4.1 although even the (weak) maximum principle fails. By using this existence result, it is shown that the ABP type maximum principle and the weak Harnack inequality for viscosity solutions hold true. As an application, the Hölder continuity for viscosity solutions of possibly singular, quasilinear equations is established.
KW - ABP maximum principle
KW - Weak Harnack inequality
KW - p-Laplace operator
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U2 - 10.1016/j.na.2017.03.018
DO - 10.1016/j.na.2017.03.018
M3 - Article
AN - SCOPUS:85019993995
SN - 0362-546X
VL - 160
SP - 1
EP - 15
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -