In this paper,we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases.We first give a full characterization of the existence of trace spac...In this paper,we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases.We first give a full characterization of the existence of trace spaces for these weighted Sobolev spaces,and then study the trace parts and the extension parts between the weighted Sobolev spaces and a new kind of Besov-type spaces(on hyperplanes)which are defined by using integral averages over selected layers of dyadic cubes.展开更多
This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge–Ampère equation det D^2u(x) = b(x)f(u(x)), u >0, x∈Ω, where Ω is a strictly convex and bounded smooth doma...This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge–Ampère equation det D^2u(x) = b(x)f(u(x)), u >0, x∈Ω, where Ω is a strictly convex and bounded smooth domain in R^N with N ≥ 2, f is normalized regularly varying at infinity with the critical index N and has a lower term, and b∈C~∞(Ω) is positive in Ω, but may be appropriate singular on the boundary.展开更多
基金partly supported by NNSF of China(Grant No.11822105)partly supported by NNSF of China(Grant Nos.12071121 and 11720101003)supported by NNSF of China(Grant No.12101226)。
文摘In this paper,we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases.We first give a full characterization of the existence of trace spaces for these weighted Sobolev spaces,and then study the trace parts and the extension parts between the weighted Sobolev spaces and a new kind of Besov-type spaces(on hyperplanes)which are defined by using integral averages over selected layers of dyadic cubes.
基金supported by NSF of P.R.China(Grant No.11571295)
文摘This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge–Ampère equation det D^2u(x) = b(x)f(u(x)), u >0, x∈Ω, where Ω is a strictly convex and bounded smooth domain in R^N with N ≥ 2, f is normalized regularly varying at infinity with the critical index N and has a lower term, and b∈C~∞(Ω) is positive in Ω, but may be appropriate singular on the boundary.
