scholarly journals On Elliptic Operator Theory

2017 ◽  
Vol 9 (6) ◽  
pp. 144
Author(s):  
Abdalla, Salih Abdalla
Keyword(s):  
Elliptic Operator ◽  
Differential Operators ◽  
Critical Role ◽  
Elliptic Operators ◽  
Smooth Functions ◽  
Elliptic Regularity ◽  
Partial Differentiation ◽  
Mathematical Problems ◽  
Mathematical Formulas ◽  
Real Characteristic

The theory talks about partial differentiation equations. For the this reason, elliptic operators take the portion of differential operators in general Laplace operators. The operators have clear definitions through the rule that the coefficients of the highest order derivatives are positives. The above aspects imply that crucial properties, which are the main symbols, are fixed. On the other hand, they can be equivalent, meaning that they have no real characteristic directions. To expound on the above, elliptic operators are representatives of the potential theory. The reason behind this is that they often appear in the field of electrostatics and continuum mechanics. Elliptic regularity shows that their solutions tend to be smooth functions, which means that it applies if the coefficients are smooth operators. Additionally, firm state resolutions to hyperbolic and parabolic equations apply in general to solve elliptic equations. Partial differentiation equations are important mathematical formulas that apply in solving mathematical problems. The theory plays a critical role in explaining functioning of the elliptic operator as many find it a mathematical phenomenon in how efficient it is in solving problems in mathematics. The article talks about theorems and lemmas in the elliptic operator.

scholarly journals Pseudo-monotonicity and degenerated or singular elliptic operators

1998 ◽  
Vol 58 (2) ◽  
pp. 213-221 ◽  
Author(s):  
P. Drábek ◽  
A. Kufner ◽  
V. Mustonen
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Type Inequality ◽  
Elliptic Operators ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Elliptic Differential Operators

Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The result extends analogous assertions for elliptic operators.

Homogeneous Calderón–Zygmund estimates for a class of second-order elliptic operators

2014 ◽  
Vol 17 (01) ◽  
pp. 1450017 ◽  
Author(s):  
G. P. Galdi ◽  
G. Metafune ◽  
C. Spina ◽  
C. Tacelli
Keyword(s):  
Elliptic Operator ◽  
Unique Solvability ◽  
Elliptic Operators ◽  
Second Order ◽  
Poisson Problem ◽  
Second Order Elliptic Operators ◽  
Uniformly Continuous

We prove unique solvability and corresponding homogeneous Lp estimates for the Poisson problem associated to the uniformly elliptic operator [Formula: see text], provided the coefficients are bounded and uniformly continuous, and admit a (non-zero) limit as |x| goes to infinity. Some important consequences are also derived.

scholarly journals Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve

2016 ◽  
Vol 146 (6) ◽  
pp. 1115-1158 ◽  
Author(s):  
Denis Borisov ◽  
Giuseppe Cardone ◽  
Tiziana Durante
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operator ◽  
Rate Of Convergence ◽  
Elliptic Operators ◽  
Resolvent Convergence ◽  
Order Elliptic Operator ◽  
Classical Boundary ◽  
Norm Resolvent Convergence ◽  
Operator Norms ◽  
Infinite Planar

We consider an infinite planar straight strip perforated by small holes along a curve. In such a domain, we consider a general second-order elliptic operator subject to classical boundary conditions on the holes. Assuming that the perforation is non-periodic and satisfies rather weak assumptions, we describe all possible homogenized problems. Our main result is the norm-resolvent convergence of the perturbed operator to a homogenized one in various operator norms and the estimates for the rate of convergence. On the basis of the norm-resolvent convergence, we prove the convergence of the spectrum.

scholarly journals Weak Uniqueness for Elliptic Operators in ℝ3 with Time-Independent Coefficients

2006 ◽  
Vol 74 (1) ◽  
pp. 91-100
Author(s):  
Cristina Giannotti
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Operator ◽  
Elliptic Operators ◽  
Second Order ◽  
Weak Uniqueness

The author gives a proof with analytic means of weak uniqueness for the Dirichlet problem associated to a second order uniformly elliptic operator in ℝ3 with coefficients independent of the coordinate x3 and continuous in ℝ2 {0}.

scholarly journals On the resolvent existence and the separability of a hyperbolic operator with fast growing coefficients in L2(R2)

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 707-721
Author(s):  
Mussakan Muratbekov ◽  
Yerik Bayandiyev
Keyword(s):  
Detailed Analysis ◽  
Unbounded Domain ◽  
Spectral Properties ◽  
Differential Operators ◽  
Elliptic Operators ◽  
Hyperbolic Operator ◽  
Fast Growing ◽  
The Space L2

This paper studies the question of the resolvent existence, as well as, the smoothness of elements from the definition domain (separability) of a class of hyperbolic differential operators defined in an unbounded domain with greatly increasing coefficients after a closure in the space L2(R2). Such a problem was previously put forward by I.M. Gelfand for elliptic operators. Here, we note that a detailed analysis shows that when studying the spectral properties of differential operators specified in an unbounded domain, the behavior of the coefficients at infinity plays an important role.

On Variational Inequalities Driven by Elliptic Operators Not in Divergence Form

2012 ◽  
Vol 12 (3) ◽  
Author(s):  
Michele Matzeu ◽  
Raffaella Servadei
Keyword(s):  
Variational Inequalities ◽  
Elliptic Operator ◽  
Bounded Domain ◽  
Smooth Boundary ◽  
Divergence Form ◽  
Elliptic Operators

AbstractIn this paper we study semilinear variational inequalities driven by an elliptic operator not in divergence form modeled bywhere Ω is a bounded domain of RN, N ≥ 3, with smooth boundary, A is the elliptic operator, not in divergence form, given byHere a

Measurement of Metacognitive Knowledge of Self, Task, and Strategies in Mathematics

2012 ◽  
Vol 28 (3) ◽  
pp. 227-239 ◽  
Author(s):  
Anastasia Efklides ◽  
Symeon P. Vlachopoulos
Keyword(s):  
High School Students ◽  
Junior High School ◽  
Convergent Validity ◽  
Critical Role ◽  
Predictive Ability ◽  
Metacognitive Knowledge ◽  
School Students ◽  
Confirmatory Factor Analyses ◽  
Confirmatory Factor ◽  
Mathematical Problems

The present study investigated the validity of the Metacognitive Knowledge in Mathematics Questionnaire (MKMQ), which taps the (1) metacognitive knowledge of the self (easiness/fluency vs. difficulty/lack of fluency the person has had in the past in basic mathematical notions); (2) the metacognitive knowledge of tasks (easy/low demands vs. difficult/high demands mathematical tasks), and (3) the metacognitive knowledge of strategies (cognitive/metacognitive strategies, competence-enhancing strategies, and avoidance strategies that serve coping with lack of fluency in mathematical task processing). The MKMQ was first administered to 311 junior high school students (grades 7 and 9) and then to 214 university students for crossvalidation. Confirmatory factor analyses confirmed the presence of 7-first-order interrelated factors. In both samples the convergent validity was tested correlating the seven factors with measures of self-concept in mathematics and mathematical ability. Predictive ability was tested using regression analyses in which the criterion variables were mean performance and feelings of difficulty in the processing of three mathematical problems. The findings support the theoretical claim that experience of difficulty is playing a critical role in the organization of metacognitive knowledge.

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