The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations.The global regulari...The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations.The global regularities in Orlicz for the second order derivatives of the solutions of the Dirichlet problems are also given.展开更多
In this paper, we present and discuss the topology of modular spaces using the filter base and we then characterize closed subsets as well as its regularity.
Let D be the open unit disk in the complex plane C. For a〉 -1, let dAa（z）=（1 ＋a） （1 -｜z}^2） ^a da（z）be the weighted Lebesgue measure on ]D. For a positive function ω ∈ L^1（D,dAa）, the generalized weight...Let D be the open unit disk in the complex plane C. For a〉 -1, let dAa（z）=（1 ＋a） （1 -｜z}^2） ^a da（z）be the weighted Lebesgue measure on ]D. For a positive function ω ∈ L^1（D,dAa）, the generalized weighted Bergman-Orlicz spaceA^ψω（D,dAa）is｜｜f｜｜ω^ψ=∫Dψ｜F（z）｜ω（z）dA^（z） 〈 ∞,where q; is a strictly convex Orlicz function that satisfies other technical hypotheses. Let G be a measurable subset of D, we say G satisfies the reverse Carleson condition for A^ψω （D, dAa） if there exists a positive constant C such that ∫Gψ（f（z））ω（z）dAa（z）≥C∫Dψ（｜f（z）dAa（z）.for all f ∈ .A^ψω （D,dAa）. Let μ be a positive Borel measure, we say μ satisfies the direct Carleson condition if there exists a positive constant M such that for all f∈Aψ^ω （D,dAa）,∫Dψ（｜f（z）｜）dμ（z）≤M∫Dψ（｜f（z）｜）ω（z）dAa（a）.In this paper, we study the direct and reverse Carleson condition on the generalized weighted Bergman-Orlicz space Aω^ψ（D,dAa）.We present conditions on the set G such that＇the reverse Carleson condition＇holds. ＂Moreover, we give a sufficient condition for the finite positive Borel measure μ to satisfy the direct carleson condition on the generalized weighted Bergman-Orlicz spaces.展开更多
We establish the existence theorem of three nontrivial solutions for a class of semilinear elliptic equation on RN by using variational theorems of mixed type due to Marino and Saccon and linking theorem.
基金Supported by the NNSF of China(10771110,11171306)Supported by the the New Century 151 Talent Project of Zhejiang Province
文摘The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations.The global regularities in Orlicz for the second order derivatives of the solutions of the Dirichlet problems are also given.
文摘In this paper, we present and discuss the topology of modular spaces using the filter base and we then characterize closed subsets as well as its regularity.
文摘Let D be the open unit disk in the complex plane C. For a〉 -1, let dAa（z）=（1 ＋a） （1 -｜z}^2） ^a da（z）be the weighted Lebesgue measure on ]D. For a positive function ω ∈ L^1（D,dAa）, the generalized weighted Bergman-Orlicz spaceA^ψω（D,dAa）is｜｜f｜｜ω^ψ=∫Dψ｜F（z）｜ω（z）dA^（z） 〈 ∞,where q; is a strictly convex Orlicz function that satisfies other technical hypotheses. Let G be a measurable subset of D, we say G satisfies the reverse Carleson condition for A^ψω （D, dAa） if there exists a positive constant C such that ∫Gψ（f（z））ω（z）dAa（z）≥C∫Dψ（｜f（z）dAa（z）.for all f ∈ .A^ψω （D,dAa）. Let μ be a positive Borel measure, we say μ satisfies the direct Carleson condition if there exists a positive constant M such that for all f∈Aψ^ω （D,dAa）,∫Dψ（｜f（z）｜）dμ（z）≤M∫Dψ（｜f（z）｜）ω（z）dAa（a）.In this paper, we study the direct and reverse Carleson condition on the generalized weighted Bergman-Orlicz space Aω^ψ（D,dAa）.We present conditions on the set G such that＇the reverse Carleson condition＇holds. ＂Moreover, we give a sufficient condition for the finite positive Borel measure μ to satisfy the direct carleson condition on the generalized weighted Bergman-Orlicz spaces.
文摘研究环的Ore扩张的幂零p.p.性,幂零Baer性和弱Mc Coy性,主要证明了:设R是一个拟IFP和(α,δ)-condition环,则有(1)如果R是幂零p.p.-环,则R[x;α,δ]是幂零p.p.-环;(2)如果R是幂零Baer环,则R[x;α,δ]是幂零Baer环;(3)R[x;α,δ]是右弱M c Coy环。
文摘We establish the existence theorem of three nontrivial solutions for a class of semilinear elliptic equation on RN by using variational theorems of mixed type due to Marino and Saccon and linking theorem.
