TY - JOUR
T1 - Weak Harnack inequality for fully nonlinear uniformly elliptic pde with unbounded ingredients
AU - Koike, Shigeaki
AU - Świȩch, Andrzej
PY - 2009/7
Y1 - 2009/7
N2 - The weak Harnack inequality for Lp-viscosity solutions is shown for fully nonlinear, second order uniformly elliptic partial differential equations with unbounded coefficients and inhomogeneous terms. This result extends those of Trudinger for strong solutions [21] and Fok for L p-viscosity solutions [13]. The proof is a modification of that of Caffarelli [5], [6], We apply the weak Harnack inequality to obtain the strong maximum principle, boundary weak Harnack inequality, global Cα estimates for solutions of fully nonlinear equations, strong solvability of extremal equations with unbounded coefficients, and Aleksandrov-Bakelman-Pucci maximum principle in unbounded domains.
AB - The weak Harnack inequality for Lp-viscosity solutions is shown for fully nonlinear, second order uniformly elliptic partial differential equations with unbounded coefficients and inhomogeneous terms. This result extends those of Trudinger for strong solutions [21] and Fok for L p-viscosity solutions [13]. The proof is a modification of that of Caffarelli [5], [6], We apply the weak Harnack inequality to obtain the strong maximum principle, boundary weak Harnack inequality, global Cα estimates for solutions of fully nonlinear equations, strong solvability of extremal equations with unbounded coefficients, and Aleksandrov-Bakelman-Pucci maximum principle in unbounded domains.
KW - Lviscosity solution
KW - Weak Harnack inequality
UR - http://www.scopus.com/inward/record.url?scp=72149133348&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=72149133348&partnerID=8YFLogxK
U2 - 10.2969/jmsj/06130723
DO - 10.2969/jmsj/06130723
M3 - Article
AN - SCOPUS:72149133348
VL - 61
SP - 723
EP - 755
JO - Journal of the Mathematical Society of Japan
JF - Journal of the Mathematical Society of Japan
SN - 0025-5645
IS - 3
ER -