Spatial Besov regularity for semilinear stochastic partial differential equations on bounded Lipschitz domains
Spatial Besov regularity for semilinear stochastic partial differential equations on bounded Lipschitz domains
复制标题
有界 Lipschitz 域上半线性随机偏微分方程的空间 Besov 正则
DOI：
10.1080/00207160.2011.631530
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发表时间：
2012
影响因子：
1.8
通讯作者：
Stephan Dahlke
中科院分区：
文献类型：
--
作者：
P. A. Cioica;Stephan Dahlke
我们研究了有界Lipschitz域上半线性抛物型随机偏微分方程的空间规律性?⊆ℝd，尺度为1/τ=α/d+1/p，p≥2固定。该尺度的贝索夫平滑度决定了自适应数值算法和其他非线性近似方案可以实现的收敛阶数。通过建立加权 Sobolev 估计并将其与 Besov 空间的小波表征相结合来进行证明。
We study the spatial regularity of semilinear parabolic stochastic partial differential equations on bounded Lipschitz domains ?⊆ ℝ d in the scale , 1/τ=α/d+1/p, p≥2 fixed. The Besov smoothness in this scale determines the order of convergence that can be achieved by adaptive numerical algorithms and other nonlinear approximation schemes. The proofs are performed by establishing weighted Sobolev estimates and combining them with wavelet characterizations of Besov spaces.