scholarly journals Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order

1967 ◽  
Vol 43 (2) ◽  
pp. 82-86 ◽  
Author(s):  
Daisuke Fujiwara
Keyword(s):  
Differential Operators ◽  
Second Order ◽  
Fractional Powers ◽  
Elliptic Differential Operators ◽  
Concrete Characterization

scholarly journals A CHARACTERIZATION OF SECOND-ORDER DIFFERENTIAL OPERATORS ON FINITE ELEMENT SPACES

2004 ◽  
Vol 14 (12) ◽  
pp. 1881-1892 ◽  
Author(s):  
SNORRE H. CHRISTIANSEN
Keyword(s):  
Finite Element ◽  
Differential Operators ◽  
Linear Differential Operator ◽  
Second Order ◽  
Unified Framework ◽  
Regge Calculus ◽  
Edge Elements ◽  
Computational Electromagnetism ◽  
Linear Differential

We describe all operators on scalar finite element spaces which appear as the restriction of a second-order (linear) differential operator. More precisely we provide a family of isomorphisms between this space of discrete differential operators and products of some exotic finite element spaces. This provides a unified framework for the Regge calculus of numerical relativity and the Nédélec edge elements of computational electromagnetism.

Oscillation criteria of Nehari-type for Sturm–Liouville operators and elliptic differential operators of second order and the lower spectrum

1988 ◽  
Vol 109 (1-2) ◽  
pp. 127-144 ◽  
Author(s):  
F. Fiedler
Keyword(s):  
Differential Equation ◽  
Differential Operators ◽  
Second Order ◽  
Oscillation Criteria ◽  
Elliptic Differential Equations ◽  
Ordinary Differential Operators ◽  
Elliptic Differential Operators ◽  
Sturm Liouville ◽  
Lower Spectrum ◽  
Liouville Operators

SynopsisSufficient oscillation criteria of Nehari-type are established for the differential equation −uʺ(t) + q(t)u(t) = 0, 0<t<∞, with and without sign restrictions on q(t), respectively. These results are extended to Sturm-Liouville equations and elliptic differential equations of second order.In Section 7 we present conclusions for the lower spectrum of elliptic differential operators and also for the discreteness of the spectrum of certain ordinary differential operators of second order.

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