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PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE S_Q(T)(1≤Q≤∞)
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作者 徐艳艳 陈广贵 +1 位作者 甘莹 许燕 《Acta Mathematica Scientia》 SCIE CSCD 2015年第2期495-507,共13页
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
关键词 Probabilistic linear width Average linear width Gaussian measure sobolevspace linear operator
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Existence of Solutions to a Semilinear Elliptic System Through Generalized Orlicz-Sobolev Spaces
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作者 HSINI M. 《Journal of Partial Differential Equations》 2010年第2期168-193,共26页
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.
关键词 Laplace operator N-FUNCTION generalized Orlicz space generalized Orlicz sobolevspace Orlicz indices Boyd exponents.
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WELL-POSEDNESS AND SPACE-TIME REGULARITY OF SOLUTIONS TO THE LIQUID CRYSTAL EQUATIONS IN CRITICAL SPACE
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作者 Congchong Guo 《Annals of Applied Mathematics》 2016年第4期357-379,共23页
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.
关键词 space-time regularity liquid crystal system critical sobolevspace
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