A difference analogue of the imbedding theorem for the anisotropic Sobolev space $$\mathop {W_{p_1 , \ldots ,p_n }^1 }\limits^0 $$

1989 ◽  
Vol 41 (7) ◽  
pp. 837-841
Author(s):  
I. M. Kolodii ◽  
I. I. Verba
Keyword(s):  
Sobolev Space ◽  
Anisotropic Sobolev Space ◽  
Difference Analogue

scholarly journals Decay of correlations in suspension semi-flows of angle-multiplying maps

2008 ◽  
Vol 28 (1) ◽  
pp. 291-317 ◽  
Author(s):  
MASATO TSUJII
Keyword(s):  
Hilbert Space ◽  
Sobolev Space ◽  
Spectral Radius ◽  
Decay Of Correlations ◽  
Square Root ◽  
Precise Description ◽  
Anisotropic Sobolev Space ◽  
Essential Spectral Radius ◽  
Frobenius Operator ◽  
Dense Set

AbstractWe consider suspension semi-flows of angle-multiplying maps on the circle for Cr ceiling functions with r≥3. Under a Crgeneric condition on the ceiling function, we show that there exists a Hilbert space (anisotropic Sobolev space) contained in the L2 space such that the Perron–Frobenius operator for the time-t-map acts naturally on it and that the essential spectral radius of that action is bounded by the square root of the inverse of the minimum expansion rate. This leads to a precise description of decay of correlations. Furthermore, the Perron–Frobenius operator for the time-t-map is quasi-compact for a Cr open and dense set of ceiling functions.

On a class of nonlinear anisotropic parabolic problems

2015 ◽  
Vol 146 (1) ◽  
pp. 1-21 ◽  
Author(s):  
M. H. Abdou ◽  
M. Chrif ◽  
S. El Manouni ◽  
H. Hjiaj
Keyword(s):  
Sobolev Space ◽  
Parabolic Problem ◽  
Nonlinear Term ◽  
Parabolic Problems ◽  
Anisotropic Sobolev Space ◽  
Existence Of Weak Solutions ◽  
Strongly Nonlinear ◽  
Nonlinear Parabolic ◽  
Sign Conditions ◽  
Image Position

We prove the existence of weak solutions for the strongly nonlinear parabolic problem in the anisotropic Sobolev space , where the data f are assumed to be in the dual, and the nonlinear term g(x, t, s) has growth and sign conditions on s.

On Krylov’s estimates for optional semimartingales

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
M. Abdelghani ◽  
A. Melnikov ◽  
A. Pak
Keyword(s):  
Sobolev Space ◽  
Measurable Function ◽  
Diffusion Processes ◽  
Stochastic Integrals ◽  
Controlled Diffusion ◽  
Convergence Of Solutions ◽  
Change Of Variables ◽  
General Class Of Functions ◽  
Class Of Functions ◽  
Controlled Diffusion Processes

Abstract The estimates of N. V. Krylov for distributions of stochastic integrals by means of the L d {L_{d}} -norm of a measurable function are well-known and are widely used in the theory of stochastic differential equations and controlled diffusion processes. We generalize estimates of this type for optional semimartingales, then apply these estimates to prove the change of variables formula for a general class of functions from the Sobolev space W d 2 {W^{2}_{d}} . We also show how to use these estimates for the investigation of L 2 {L^{2}} -convergence of solutions of optional SDE’s.

On the convergence of difference schemes for the generalized BBM–Burgers equation

2019 ◽  
Vol 26 (3) ◽  
pp. 341-349 ◽  
Author(s):  
Givi Berikelashvili ◽  
Manana Mirianashvili
Keyword(s):  
Exact Solution ◽  
Sobolev Space ◽  
Difference Scheme ◽  
Absolute Stability ◽  
Burgers Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Algebraic Equations ◽  
The Difference ◽  
Initial Boundary Value

Abstract A three-level finite difference scheme is studied for the initial-boundary value problem of the generalized Benjamin–Bona–Mahony–Burgers equation. The obtained algebraic equations are linear with respect to the values of the desired function for each new level. The unique solvability and absolute stability of the difference scheme are shown. It is proved that the scheme is convergent with the rate of order {k-1} when the exact solution belongs to the Sobolev space {W_{2}^{k}(Q)} , {1<k\leq 3} .

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