On a Double Integral Variational Problem

1954 ◽  
Vol 6 ◽  
pp. 441-446 ◽  
Author(s):  
P. R. Garabedian ◽  
M. Schiffer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Equation Of State ◽  
Convex Function ◽  
Variational Problem ◽  
Compressible Fluid ◽  
Subsonic Flow ◽  
Elliptic Partial Differential Equation ◽  
Double Integral ◽  
Image Position

The results presented here were motivated by a desire to give a simple treatment of the non-linear elliptic partial differential equation governing the steady irrotational subsonic flow of an ideal compressible fluid. For two independent space variables x and y, the stream function Ψ of such a flow satisfies an equation,where is an analytic, increasing, convex function of whose explicit form depends on the equation of state of the fluid in question.

Nonoscillation Criteria for Elliptic Equations

1969 ◽  
Vol 12 (3) ◽  
pp. 275-280 ◽  
Author(s):  
C.A. Swanson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Elliptic Equations ◽  
Sufficient Conditions ◽  
Elliptic Partial Differential Equation ◽  
Dimensional Euclidean Space ◽  
Normal Vector ◽  
Unit Normal Vector ◽  
Piecewise Continuous ◽  
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Sufficient conditions will be derived for the linear elliptic partial differential equation(1)to be nonoscillatory in an unbounded domain R in n-dimensional Euclidean space En. The boundary ∂R of R is supposed to have a piecewise continuous unit normal vector at each point. There is no essential loss of generality in assuming that R contains the origin. Otherwise no special assumptions are needed regarding the shape of R: it is not necessary for R to be quasiconical (as in [2]), quasicylindrical, or quasibounded [1].

Oscillation of Elliptic Equations in General Domains

1975 ◽  
Vol 27 (6) ◽  
pp. 1239-1245 ◽  
Author(s):  
E. S. Noussair
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Operator ◽  
Euclidean Space ◽  
Unbounded Domain ◽  
Elliptic Equations ◽  
General Type ◽  
Elliptic Partial Differential Equation ◽  
Dimensional Euclidean Space ◽  
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Oscillation criteria will be obtained for the linear elliptic partial differential equationin an unbounded domain G of general type in n-dimensional Euclidean space En. The differential operator D is defined as usual by where each α (i), i = 1, … , n, is a non-negative integer.

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