Local a priori estimates in Lp for first order linear operators with nonsmooth coefficients

1997 ◽  
Vol 94 (1) ◽  
pp. 151-167 ◽  
Author(s):  
Jorge Hounie ◽  
Maria Eulália Moraes Melo
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Linear Operators ◽  
Order Linear ◽  
First Order ◽  
Priori Estimates ◽  
Nonsmooth Coefficients

scholarly journals FIRST-ORDER METHODS FOR GENERALIZED OPTIMAL CONTROL PROBLEMS FOR SYSTEMS WITH DISTRIBUTED PARAMETERS

2020 ◽  
pp. 18-44
Author(s):  
S. V. Denisov ◽  
V. V. Semenov
Keyword(s):  
Optimal Control Problems ◽  
A Priori Estimates ◽  
A Priori ◽  
Control Problems ◽  
First Order ◽  
Admissible Sets ◽  
Distributed Parameters ◽  
Priori Estimates ◽  
Systems With Distributed Parameters ◽  
First Order Methods

The problems of optimization of linear distributed systems with generalized control and first-order methods for their solution are considered. The main focus is on proving the convergence of methods. It is assumed that the operator describing the model satisfies a priori estimates in negative norms. For control problems with convex and preconvex admissible sets, the convergence of several first-order algorithms with errors in iterative subproblems is proved.

scholarly journals COEFFICIENT STABILITY OF OPERATOR–DIFFERENCE SCHEMES

1999 ◽  
Vol 4 (1) ◽  
pp. 135-146
Author(s):  
P. P. Matus ◽  
B. S. Jovanović
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Difference Schemes ◽  
Evolutionary Equation ◽  
Finite Difference Schemes ◽  
Initial Condition ◽  
First Order ◽  
Time Integral ◽  
Priori Estimates ◽  
Coefficient Stability

A priori estimates expressing continuous dependence of the solution of a first order evolutionary equation in Hubert space on initial condition, right hand side and operator perturbations are obtained in time–integral norms. Analogous results hold for corresponding finite difference schemes.

DISCONTINUOUS/CONTINUOUS LEAST-SQUARES FINITE ELEMENT METHODS FOR ELLIPTIC PROBLEMS

2005 ◽  
Vol 15 (06) ◽  
pp. 825-842 ◽  
Author(s):  
RICKARD E. BENSOW ◽  
MATS G. LARSON
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Finite Element Methods ◽  
A Priori Estimates ◽  
A Priori ◽  
Solution Space ◽  
First Order ◽  
Poisson Problem ◽  
Priori Estimates ◽  
The Stability

Least-squares finite element methods (LSFEM) are useful for first-order systems, where they avoid the stability consideration of mixed methods and problems with constraints, like the div-curl problem. However, LSFEM typically suffer from requirements on the solution to be very regular. This rules out, e.g., applications posed on nonconvex domains. In this paper we study a least-squares formulation where the discrete space is enriched by discontinuous elements in the vicinity of singularities. The weighting on the interelement terms are chosen to give correct regularity of the solution space and thus making computation of less regular problems possible. We apply this technique to the first-order Poisson problem, show coercivity and a priori estimates, and present numerical results in 3D.

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

Convergence of the Rosenau-Korteweg-de Vries Equation to the Korteweg-de Vries One

2020 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
A Priori Estimates ◽  
Vries Equation ◽  
A Priori ◽  
Diffusion Parameter ◽  
Priori Estimates ◽  
De Vries ◽  
Wall Interactions

The Rosenau-Korteweg-de Vries equation describes the wave-wave and wave-wall interactions. In this paper, we prove that, as the diffusion parameter is near zero, it coincides with the Korteweg-de Vries equation. The proof relies on deriving suitable a priori estimates together with an application of the Aubin-Lions Lemma.

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