In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional d...In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.展开更多
The paper is devoted to the homogenization of elliptic systems in divergence form.We obtain uniform interior as well as boundary Lipschitz estimates in a bounded C1,γdomain when the coefficients are Dini continuous,i...The paper is devoted to the homogenization of elliptic systems in divergence form.We obtain uniform interior as well as boundary Lipschitz estimates in a bounded C1,γdomain when the coefficients are Dini continuous,inhomogeneous terms are divergence of Dini continuous functions and the boundary functions have Dini continuous derivatives.The results extend Avellaneda and Lin’s work[Comm.Pure Appl.Math.,40:803-847(1987)],where Holder continuity is the main assumption on smoothness of the data.展开更多
Interior regularity results for viscosity solutions of fully nonlinear uniformly parabolic equations under the Dini condition, which improve and generalize a result due to Kovats, are obtained by the use of the approx...Interior regularity results for viscosity solutions of fully nonlinear uniformly parabolic equations under the Dini condition, which improve and generalize a result due to Kovats, are obtained by the use of the approximation lemma.展开更多
本文研究了Marcinkiewicz积分交换子μΩ,b(f)(x)=(integral from n=0 to ∞|Fb,t(f)(x)|2 dt/t3)1/2, 其中Fb,t(f)(x)=integral from n=|x-y|≤t(Ω(x-y_/|x-y|n-1)b(x)-b(y)f(y)dy及b∈Λβ,证明了算子μΩ,b是Lp(Rn) 到Fβ,∞p(Rn)...本文研究了Marcinkiewicz积分交换子μΩ,b(f)(x)=(integral from n=0 to ∞|Fb,t(f)(x)|2 dt/t3)1/2, 其中Fb,t(f)(x)=integral from n=|x-y|≤t(Ω(x-y_/|x-y|n-1)b(x)-b(y)f(y)dy及b∈Λβ,证明了算子μΩ,b是Lp(Rn) 到Fβ,∞p(Rn)上的有界算子并且也是Lp(Rn)到Lq(Rn)上的有界算子.展开更多
基金The Graduate Students Innovate Scientific Research Program (YJSCX2008-158HLJ) of Heilongjiang Provincesupported by the Distinguished Young Scholar Foundation (JC200707) of Heilongjiang Province of China
文摘In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.
基金Supported in part by the National Natural Science Foundation of China(No.12071365 and 12001419)。
文摘The paper is devoted to the homogenization of elliptic systems in divergence form.We obtain uniform interior as well as boundary Lipschitz estimates in a bounded C1,γdomain when the coefficients are Dini continuous,inhomogeneous terms are divergence of Dini continuous functions and the boundary functions have Dini continuous derivatives.The results extend Avellaneda and Lin’s work[Comm.Pure Appl.Math.,40:803-847(1987)],where Holder continuity is the main assumption on smoothness of the data.
文摘Interior regularity results for viscosity solutions of fully nonlinear uniformly parabolic equations under the Dini condition, which improve and generalize a result due to Kovats, are obtained by the use of the approximation lemma.
文摘本文研究了Marcinkiewicz积分交换子μΩ,b(f)(x)=(integral from n=0 to ∞|Fb,t(f)(x)|2 dt/t3)1/2, 其中Fb,t(f)(x)=integral from n=|x-y|≤t(Ω(x-y_/|x-y|n-1)b(x)-b(y)f(y)dy及b∈Λβ,证明了算子μΩ,b是Lp(Rn) 到Fβ,∞p(Rn)上的有界算子并且也是Lp(Rn)到Lq(Rn)上的有界算子.
