This paper is concerned with exact boundary behavior of large solutions to semilinear elliptic equations △u=b(x)f(u)(C0+|▽u|q),x∈Ω,where Ω is a bounded domain with a smooth boundary in RN,C0≥0,q E [0,2),b∈Cloc...This paper is concerned with exact boundary behavior of large solutions to semilinear elliptic equations △u=b(x)f(u)(C0+|▽u|q),x∈Ω,where Ω is a bounded domain with a smooth boundary in RN,C0≥0,q E [0,2),b∈Clocα(Ω) is positive in but may be vanishing or appropriately singular on the boundary,f∈C[0,∞),f(0)=0,and f is strictly increasing on [0,∞)(or f∈C(R),f(s)> 0,■s∈R,f is strictly increasing on R).We show unified boundary behavior of such solutions to the problem under a new structure condition on f.展开更多
This paper is concerned with the existence and optimal boundary behavior of large solutions to the Monge-Ampère type equations det D^(2)u(x)=λu^(n)(x)+b(x)g(|▽u(x)|),x∈Ω,where Ω is a uniformly convex,bounded...This paper is concerned with the existence and optimal boundary behavior of large solutions to the Monge-Ampère type equations det D^(2)u(x)=λu^(n)(x)+b(x)g(|▽u(x)|),x∈Ω,where Ω is a uniformly convex,bounded smooth domain in R^(n) with n≥2,b∈C^(∞)(Ω) is positive in Ω,g∈C[0,∞)∩C^(1)(0,∞),g(0)=0 and g is increasing on[0,∞).The author finds new structure conditions on g which play a crucial role in boundary behavior of such solutions.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11571295)
文摘This paper is concerned with exact boundary behavior of large solutions to semilinear elliptic equations △u=b(x)f(u)(C0+|▽u|q),x∈Ω,where Ω is a bounded domain with a smooth boundary in RN,C0≥0,q E [0,2),b∈Clocα(Ω) is positive in but may be vanishing or appropriately singular on the boundary,f∈C[0,∞),f(0)=0,and f is strictly increasing on [0,∞)(or f∈C(R),f(s)> 0,■s∈R,f is strictly increasing on R).We show unified boundary behavior of such solutions to the problem under a new structure condition on f.
基金supported by Shandong Provincial Natural Science Foundation(Nos.ZR2021MA007,ZR2022MA020)。
文摘This paper is concerned with the existence and optimal boundary behavior of large solutions to the Monge-Ampère type equations det D^(2)u(x)=λu^(n)(x)+b(x)g(|▽u(x)|),x∈Ω,where Ω is a uniformly convex,bounded smooth domain in R^(n) with n≥2,b∈C^(∞)(Ω) is positive in Ω,g∈C[0,∞)∩C^(1)(0,∞),g(0)=0 and g is increasing on[0,∞).The author finds new structure conditions on g which play a crucial role in boundary behavior of such solutions.
