Flat wavelet bases adapted to the homogeneous Sobolev spaces

2008 ◽  
Vol 282 (1) ◽  
pp. 104-124 ◽  
Author(s):  
Béatrice Vedel
Keyword(s):  
Sobolev Spaces ◽  
Wavelet Bases ◽  
Homogeneous Sobolev Spaces

scholarly journals Viscous Flow Around a Rigid Body Performing a Time-periodic Motion

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Thomas Eiter ◽  
Mads Kyed
Keyword(s):  
Rigid Body ◽  
Sobolev Spaces ◽  
Periodic Motion ◽  
Viscous Incompressible Fluid ◽  
Body Motion ◽  
Translational Velocity ◽  
Ill Posed ◽  
Homogeneous Sobolev Spaces ◽  
The Mean ◽  
Time Periodic

AbstractThe equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.

Bilinear forms on non-homogeneous Sobolev spaces

2020 ◽  
Vol 32 (4) ◽  
pp. 995-1026
Author(s):  
Carme Cascante ◽  
Joaquín M. Ortega
Keyword(s):  
Sobolev Spaces ◽  
Bilinear Form ◽  
Positive Measure ◽  
Bilinear Forms ◽  
Homogeneous Sobolev Spaces

AbstractIn this paper, we show that if {b\in L^{2}(\mathbb{R}^{n})}, then the bilinear form defined on the product of the non-homogeneous Sobolev spaces {H_{s}^{2}(\mathbb{R}^{n})\times H_{s}^{2}(\mathbb{R}^{n})}, {0<s<1}, by(f,g)\in H_{s}^{2}(\mathbb{R}^{n})\times H_{s}^{2}(\mathbb{R}^{n})\to\int_{% \mathbb{R}^{n}}(\mathrm{Id}-\Delta)^{\frac{s}{2}}(fg)(\mathbf{x})b(\mathbf{x})% \mathop{}\!d\mathbf{x}is continuous if and only if the positive measure {\lvert b(\mathbf{x})\rvert^{2}\mathop{}\!d\mathbf{x}} is a trace measure for {H_{s}^{2}(\mathbb{R}^{n})}.

scholarly journals Bilinear forms on homogeneous Sobolev spaces

2018 ◽  
Vol 457 (1) ◽  
pp. 722-750
Author(s):  
Carme Cascante ◽  
Joan Fàbrega ◽  
Joaquín M. Ortega
Keyword(s):  
Sobolev Spaces ◽  
Bilinear Forms ◽  
Homogeneous Sobolev Spaces

scholarly journals Fractional Laplacian, homogeneous Sobolev spaces and their realizations

2020 ◽  
Vol 199 (6) ◽  
pp. 2243-2261 ◽  
Author(s):  
Alessandro Monguzzi ◽  
Marco M. Peloso ◽  
Maura Salvatori
Keyword(s):  
Sobolev Spaces ◽  
Fractional Laplacian ◽  
Homogeneous Sobolev Spaces

scholarly journals Compactly supported wavelet bases for Sobolev spaces

2003 ◽  
Vol 15 (3) ◽  
pp. 224-241 ◽  
Author(s):  
Rong-Qing Jia ◽  
Jianzhong Wang ◽  
Ding-Xuan Zhou
Keyword(s):  
Sobolev Spaces ◽  
Wavelet Bases ◽  
Compactly Supported

M-CHANNEL MRA AND APPLICATION TO ANISOTROPIC SOBOLEV SPACES

2005 ◽  
Vol 03 (02) ◽  
pp. 153-166
Author(s):  
ELENA CORDERO
Keyword(s):  
Tensor Product ◽  
Sobolev Spaces ◽  
Unit Interval ◽  
Biorthogonal Wavelet ◽  
Bernstein Type ◽  
Wavelet Bases ◽  
Compactly Supported ◽  
Anisotropic Sobolev Spaces ◽  
Dilation Factor ◽  
Bernstein Type Inequalities

In this paper we construct compactly supported biorthogonal wavelet bases of the interval, with dilation factor M. Next, the natural MRA on the cube arising from the tensor product of a multilevel decomposition of the unit interval is developed. New Jackson and Bernstein type inequalities are proved, providing a characterization for anisotropic Sobolev spaces.

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