Probabilistic linear (N, δ)-widths and p-average linear N-widths of Sobolev space W2^r(T), equipped with a Gaussian probability measure #, are studied in the metric of Sq (T) (1 ≤ Q ≤∞), and determined the...Probabilistic linear (N, δ)-widths and p-average linear N-widths of Sobolev space W2^r(T), equipped with a Gaussian probability measure #, are studied in the metric of Sq (T) (1 ≤ Q ≤∞), and determined the asymptotic equalities:λN,δ(W2^r(T),μ,Sq(T))={(N^-1)^r+p/2-1/q√1+1/N·ln1/δ, 1≤q≤2, (N^-1)^r+p/2-1/q(1+N^-1/q√ln1/δ),2〈q〈∞, (N^-1)^r+p/2√lnN/δ, q=∞,and λN^(a)(W2^r(T),μ,Sq(T))p={(N^-1)^r+p/2-1/q, 1≤q〈∞, (N^-1)^r+p/2-1/q√lnN, q=∞,where 0 〈 p 〈 ∞, δ∈ (0, 1/2], ρ 〉 1, and Sq(T) is a subspace of L1(T), in which the Fourier series is absolutely convergent in lq sense.展开更多
This paper is concerned with the existence theory of a semilinear elliptic system. In particular, we will prove that the system has a nontrivial positive solution in some appropriate solution spaces.
In this paper, we consider a hydrodynamic flow of nematic liquid crystal system. We prove the local well-posedness for the system in the critical Lebesgue space, and study the space-time regularity of the local solution.
基金partially supported by National Nature Science Foundation of China(61372187)Sichuan Key Technology Research and Development Program(2012GZ0019,2013GXZ0155)the Fund of Lab of Security Insurance of Cyberspace,Sichuan Province(szjj2014-079)
文摘Probabilistic linear (N, δ)-widths and p-average linear N-widths of Sobolev space W2^r(T), equipped with a Gaussian probability measure #, are studied in the metric of Sq (T) (1 ≤ Q ≤∞), and determined the asymptotic equalities:λN,δ(W2^r(T),μ,Sq(T))={(N^-1)^r+p/2-1/q√1+1/N·ln1/δ, 1≤q≤2, (N^-1)^r+p/2-1/q(1+N^-1/q√ln1/δ),2〈q〈∞, (N^-1)^r+p/2√lnN/δ, q=∞,and λN^(a)(W2^r(T),μ,Sq(T))p={(N^-1)^r+p/2-1/q, 1≤q〈∞, (N^-1)^r+p/2-1/q√lnN, q=∞,where 0 〈 p 〈 ∞, δ∈ (0, 1/2], ρ 〉 1, and Sq(T) is a subspace of L1(T), in which the Fourier series is absolutely convergent in lq sense.
文摘This paper is concerned with the existence theory of a semilinear elliptic system. In particular, we will prove that the system has a nontrivial positive solution in some appropriate solution spaces.
文摘In this paper, we consider a hydrodynamic flow of nematic liquid crystal system. We prove the local well-posedness for the system in the critical Lebesgue space, and study the space-time regularity of the local solution.