In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)^(α)Ω on a bounded open set Ω ■R(N ≥ 2) with C^((1,1)) boundary ■Ω...In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)^(α)Ω on a bounded open set Ω ■R(N ≥ 2) with C^((1,1)) boundary ■Ω. We prove that when f ∈ L^(p)(Ω), and g ∈ C(Ω), the following problem (-△)^(α)Ωu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W^((α,2))(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn.展开更多
We obtained the Cα continuity for weak solutions of a class of ultraparabolic equations with measurable coeffcients of the form δt u = δx（a（x, y, t）δx u） ＋ b0（x, y, t）δxu ＋ b（x, y, t）δyu, which general...We obtained the Cα continuity for weak solutions of a class of ultraparabolic equations with measurable coeffcients of the form δt u = δx（a（x, y, t）δx u） ＋ b0（x, y, t）δxu ＋ b（x, y, t）δyu, which generalized our recent results on KFP equations.展开更多
In this paper, the authors will apply De Giorgi-Nash-Moser iteration to establish boundary H?lder estimates for a class of degenerate elliptic equations in piecewise C^(2)-smooth domains.
基金Supported by the Natural Science Foundation of Hebei Province (Grant No. A2018210018)the Science and Technology Research Program of Higher Educational in Hebei Province (Grant No. ZD2019047)。
文摘In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)^(α)Ω on a bounded open set Ω ■R(N ≥ 2) with C^((1,1)) boundary ■Ω. We prove that when f ∈ L^(p)(Ω), and g ∈ C(Ω), the following problem (-△)^(α)Ωu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W^((α,2))(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn.
基金partially supported by the NSF of China (10325104)
文摘We obtained the Cα continuity for weak solutions of a class of ultraparabolic equations with measurable coeffcients of the form δt u = δx（a（x, y, t）δx u） ＋ b0（x, y, t）δxu ＋ b（x, y, t）δyu, which generalized our recent results on KFP equations.
基金supported by the National Natural Science Foundation of China(Nos.11631011,11871160,12141105)。
文摘In this paper, the authors will apply De Giorgi-Nash-Moser iteration to establish boundary H?lder estimates for a class of degenerate elliptic equations in piecewise C^(2)-smooth domains.
