Mohammad Alomari
Theorem: 设{Sn(x)}为函数序列,若: (1)Sn(x)在[a,b]上连续; (2){Sn(x)}在[a,b]上点态收敛于连续函数S(x); (3){Sn(x)}关于固定的x,关于n单调. 则{Sn(x)}在[a,b]上一致收敛于S(x). 反证法,若{Sn(x)}在[a,b]上非一致收敛于S(x),则推出矛盾. ...
Proof Let Theorem2.7, continuousfunc- tion uniform.Set 1min{h,1/2}, Sinceinf boundedaway from end,set convergessimply convergesuniformly ideaunderlying foregoingproof stems fromthe recursive counterexample Dini’stheorem Theorem4.8 followingfour items equivalent:FT, DT {0,1} allcompact metric spaces...
Boundary regularity results for viscosity solutions of Poisson s equation and fully nonlinear uniformly elliptic equations under the Dini condition are obtained by use of Caffarelli s perturbation method, which give a simple proof of Theorem 4. 笔者利用Caffarelli扰动方法,证明了Poisson方程和完全非线性一...
We completely characterize the Dini derivatives of any function in the Denjoy-Saks-Young Theorem. Banach's original proof of the measurability of the Dini derivatives of a measurable function is given. The chapter ends with some results on the Dini derivatives of a convex function. 展开 ...
In this paper we extend Radó-Kneser-Choquet theorem for the mappings with weak homeomorphic Lipschitz boundary function and Dini's smooth boundary but without restriction on the convexity of the image domain, provided that the Jacobian satisfies a certain boundary condition. The proof is based on ...
haveTheorem5.1: Let“∈W1m(Q,RⅣ)nL∞(Q,RⅣ) beaweaksolution of(2.2)under the assumptions(H1)一(凰),(p1)一(p2)withsupQI仳I=M.Then thereexistsa relatively closedsetSingucQitsuchthat U∈C1(f2\Singu,RⅣ).Furthermore SinguC∑1u∑2,where ∑一{Xo ...
Proof Obvious. □ Theorem 2.18 AC For a frame L, the following assertions are equivalent: (1) L is quasi-Lindelöf. (2) The coreflection of L from completely regular frames is Lindelöf. (3) For any net (αη)η∈D in RL and any f∈RL such that (αη)η∈D↑α (resp....
Remark 1.1For elliptic equations with coefficients satisfying α-increasing Dini conditions,a proof of the C1regularity of u can be found(see,e.g.,[6,Theorem 5.1]as pointed out in[1–2]). Question 1.1If we replacein(1.3)by 2 M ain Results and Proofs ...
Boundary regularity results for viscosity solutions of Poisson s equation and fully nonlinear uniformly elliptic equations under theDini conditionare obtained by use of Caffarelli s perturbation method, which give a simple proof of Theorem 4.