A compact embedding result for anisotropic Sobolev spaces associated to a strip-like domain and some applications

2019 ◽  
pp. 123490 ◽  
Author(s):  
Claudianor Alves ◽  
Giovanni Molica Bisci
Keyword(s):  
Sobolev Spaces ◽  
Compact Embedding ◽  
Anisotropic Sobolev Spaces

scholarly journals Some notes on embedding for anisotropic Sobolev spaces

2011 ◽  
Vol 61 (1) ◽  
pp. 97-111 ◽  
Author(s):  
Hongliang Li ◽  
Quinxiu Sun
Keyword(s):  
Sobolev Spaces ◽  
Anisotropic Sobolev Spaces

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.

scholarly journals On the Cauchy problems associated to a ZK-KP-type family equations with a transversal fractional dispersion

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jorge Morales Paredes ◽  
Félix Humberto Soriano Méndez
Keyword(s):  
Fractional Derivative ◽  
Sobolev Spaces ◽  
Hilbert Transform ◽  
Well Posedness ◽  
Cauchy Problems ◽  
Anisotropic Sobolev Spaces ◽  
The Hilbert Transform

<p style='text-indent:20px;'>In this paper we examine the well-posedness and ill-posedeness of the Cauchy problems associated with a family of equations of ZK-KP-type</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{cases} u_{t} = u_{xxx}-\mathscr{H}D_{x}^{\alpha}u_{yy}+uu_{x}, \cr u(0) = \psi \in Z \end{cases} $\end{document} </tex-math> </disp-formula></p><p style='text-indent:20px;'>in anisotropic Sobolev spaces, where <inline-formula><tex-math id="M1">\begin{document}$ 1\le \alpha \le 1 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ \mathscr{H} $\end{document}</tex-math></inline-formula> is the Hilbert transform and <inline-formula><tex-math id="M3">\begin{document}$ D_{x}^{\alpha} $\end{document}</tex-math></inline-formula> is the fractional derivative, both with respect to <inline-formula><tex-math id="M4">\begin{document}$ x $\end{document}</tex-math></inline-formula>.</p>

scholarly journals On Entropy Solutions of Anisotropic Elliptic Equations with Variable Nonlinearity Indices

2017 ◽  
Vol 63 (3) ◽  
pp. 475-493 ◽  
Author(s):  
L M Kozhevnikova
Keyword(s):  
Dirichlet Problem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Unbounded Domains ◽  
Second Order ◽  
Entropy Solutions ◽  
Anisotropic Sobolev Spaces ◽  
Right Hand ◽  
Anisotropic Elliptic Equations

For a certain class of second-order anisotropic elliptic equations with variable nonlinearity indices and L1 right-hand side we consider the Dirichlet problem in arbitrary unbounded domains. We prove the existence and uniqueness of entropy solutions in anisotropic Sobolev spaces with variable indices.

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