scholarly journals Regularity results for solutions of linear elliptic degenerate boundary-value problems

2020 ◽  
Vol 9 (3) ◽  
pp. 545-566
Author(s):  
A. El Baraka ◽  
M. Masrour
Keyword(s):  
Sobolev Spaces ◽  
General Framework ◽  
A Priori ◽  
A Priori Estimate ◽  
Priori Estimate ◽  
Degenerate Elliptic ◽  
Type Spaces ◽  
Order Degenerate ◽  
Regularity Results ◽  
Besov Type Spaces

Abstract We give an a-priori estimate near the boundary for solutions of a class of higher order degenerate elliptic problems in the general Besov-type spaces $$B^{s,\tau }_{p,q}$$ B p , q s , τ . This paper extends the results found in Hölder spaces $$C^s$$ C s , Sobolev spaces $$H^s$$ H s and Besov spaces $$B^s_{p,q}$$ B p , q s , to the more general framework of Besov-type spaces.

scholarly journals Erratum to: A-priori Estimates Near the Boundary for Solutions of a class of Degenerate Elliptic Problems in Besov-type Spaces; DOI 10.1515/mjpaa-2017-0013

2018 ◽  
Vol 4 (1) ◽  
pp. 44-45
Author(s):  
Azzeddine El Baraka ◽  
Mohammed Masrour
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Problems ◽  
Priori Estimates ◽  
Degenerate Elliptic ◽  
Type Spaces ◽  
Besov Type Spaces

AbstractIn this note, we point out some minor errors found in [1] and we give the proper corrections.

scholarly journals A-priori Estimates Near the Boundary for Solutions of a class of Degenerate Elliptic Problems in Besov-type Spaces

2017 ◽  
Vol 3 (2) ◽  
pp. 149-172 ◽  
Author(s):  
Azzeddine El Baraka ◽  
Mohammed Masrour
Keyword(s):  
Besov Spaces ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Problems ◽  
General Frame ◽  
Priori Estimates ◽  
Special Cases ◽  
Degenerate Elliptic ◽  
Type Spaces ◽  
Besov Type Spaces

AbstractIn this paper, we give a priori estimates near the boundary for solutions of a degenerate elliptic problems in the general Besov-type spaces $B_{p,q}^{s,\tau }$, containing as special cases: Goldberg space bmo, local Morrey-Campanato spaces l2,λ and the classical Hölder and Besov spaces $B_{p,q}^s $. This work extends the results of [13, 2, 15] from Hölder and Besov spaces to the general frame of $B_{p,q}^{s,\tau }$ spaces.

scholarly journals A PRIORI ESTIMATE FOR AN EQUATION WITH FRACTIONAL DERIVATIVES WITH DIFFERENT ORIGINS

2019 ◽  
pp. 41-47
Author(s):  
Л.М. Энеева
Keyword(s):  
Fractional Derivatives ◽  
Model Equation ◽  
A Priori ◽  
A Priori Estimate ◽  
Equation Of Motion ◽  
Point Boundary ◽  
Priori Estimate ◽  
Fractal Media ◽  
Different Origins ◽  
Variable Potential

В работе исследуется обыкновенное дифференциальное уравнение дробного порядка, содержащее композицию дробных производных с различными началами, с переменным потенциалом. Рассматриваемое уравнение выступает модельным уравнением движения во фрактальной среде. Для исследуемого уравнения доказана априорная оценка решения смешанной двухточечной краевой задачи. We consider an ordinary differential equation of fractional order with the composition of leftand right-sided fractional derivatives, and with variable potential. The considered equation is a model equation of motion in fractal media. We prove an a priori estimate for solutions of a mixed two-point boundary value problem for the equation under study.

scholarly journals A Discrete Analog of the Lyapunov Function for Hyperbolic Systems

2018 ◽  
Vol 64 (4) ◽  
pp. 591-602
Author(s):  
R D Aloev ◽  
M U Khudayberganov
Keyword(s):  
Lyapunov Function ◽  
Hyperbolic Systems ◽  
A Priori ◽  
A Priori Estimate ◽  
Discrete Analog ◽  
Priori Estimate ◽  
Constant Coefficients ◽  
The Difference ◽  
Dissipative Boundary ◽  
Linear Hyperbolic System

We study the difference splitting scheme for the numerical calculation of stable solutions of a two-dimensional linear hyperbolic system with dissipative boundary conditions in the case of constant coefficients with lower terms. A discrete analog of the Lyapunov function is constructed and an a priori estimate is obtained for it. The obtained a priori estimate allows us to assert the exponential stability of the numerical solution.

scholarly journals On a class of singular hyperbolic equation with a weighted integral condition

1999 ◽  
Vol 22 (3) ◽  
pp. 511-519 ◽  
Author(s):  
Said Mesloub ◽  
Abdelfatah Bouziani
Keyword(s):  
Hyperbolic Equation ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Nonlocal Condition ◽  
A Priori ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Priori Estimate ◽  
Weighted Integral

In this paper, we study a mixed problem with a nonlocal condition for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.

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