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In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P(D~n, B~N) is C~(1+α) at z0 ∈ E_rD~n with f(0) = 0 and f(z_0) = ω_0∈B~N for any n,N ≥ 1, then there exist a nonnegative vector λ_f =(λ_1,0,…,λ_r,0,…,0)~T∈R~(2 n)satisfying λ_i≥1/(2~(2 n-1)) for 1 ≤ i ≤ r such that where z'_0 and w'_0 are real versions of z_0 and w_0, respectively. 相似文献
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Jinhuan Wang Linghua Kong Sining Zheng 《Nonlinear Analysis: Real World Applications》2010,11(3):2136-2140
This paper deals with Cauchy problem to nonlinear diffusion with , () and Hölder continuous. A new phenomenon is observed that the critical Fujita exponent whenever . More precisely, the solution blows up under any nontrivial and nonnegative initial data for all . This result is then extended to a coupled system with localized sources as well as the cases with other nonlinearities. 相似文献
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《Journal of Complexity》2016,32(6):867-884
We are interested in approximation of a multivariate function by linear combinations of products of univariate functions , . In the case it is the classical problem of bilinear approximation. In the case of approximation in the space the bilinear approximation problem is closely related to the problem of singular value decomposition (also called Schmidt expansion) of the corresponding integral operator with the kernel . There are known results on the rate of decay of errors of best bilinear approximation in under different smoothness assumptions on . The problem of multilinear approximation (nonlinear tensor product approximation) in the case is more difficult and much less studied than the bilinear approximation problem. We will present results on best multilinear approximation in under mixed smoothness assumption on . 相似文献
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