The three-sphere theorem for a class of elliptic equations of high order and a refinement of this theorem for a linear elliptic equation of second order

1968 ◽  
pp. 135-162 ◽  
Author(s):  
Ju. K. Gerasimov
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Second Order ◽  
High Order ◽  
Sphere Theorem ◽  
Linear Elliptic Equation ◽  
Three Sphere

Identification of a constant coefficient in a quasi-linear elliptic equation

2014 ◽  
Vol 22 (3) ◽  
Author(s):  
Anna S. Lyubanova
Keyword(s):  
Differential Equation ◽  
Elliptic Equation ◽  
Constant Coefficient ◽  
Order Differential Equation ◽  
Second Order ◽  
Main Term ◽  
Linear Elliptic Equation ◽  
Unknown Constant ◽  
Second Order Differential Equation

Abstract.The identification of an unknown constant coefficient in the main term of the second order differential equation

scholarly journals On the boundary values of the solutions of linear elliptic equations

1983 ◽  
Vol 27 (1) ◽  
pp. 1-30 ◽  
Author(s):  
J. Chabrowski ◽  
H.B. Thompson
Keyword(s):  
Elliptic Equation ◽  
Sobolev Space ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Sufficient Condition ◽  
Boundary Values ◽  
Linear Elliptic Equation

The purpose of this article is to investigate the traces of weak solutions of a linear elliptic equation. In particular, we obtain a sufficient condition for a solution belonging to the Sobolev space to have an L2-trace on the boundar.

scholarly journals On Wiener's Criterion for an Elliptic Equation with Nonuniform Degeneration

2007 ◽  
Vol 14 (4) ◽  
pp. 607-626
Author(s):  
Rabil A. Amanov ◽  
Farman I. Mamedov
Keyword(s):  
Elliptic Equation ◽  
Laplace Equation ◽  
Elliptic Equations ◽  
Second Order ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Boundary Points ◽  
Necessary And Sufficient

Abstract For some class of nonuniformly degenerated elliptic equations of second order, a necessary and sufficient condition for boundary points to be regular is found. This condition is an analogue of Wiener's criterion for the Laplace equation.

scholarly journals A variant of Clark’s theorem and its applications for nonsmooth functionals without the global symmetric condition

2021 ◽  
Vol 11 (1) ◽  
pp. 285-303
Author(s):  
Chen Huang
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Linear Elliptic Equation ◽  
Clark’S Theorem

Abstract We give a new non-smooth Clark’s theorem without the global symmetric condition. The theorem can be applied to generalized quasi-linear elliptic equations with small continous perturbations. Our results improve the abstract results about a semi-linear elliptic equation in Kajikiya [10] and Li-Liu [11].

Mean value theorems for polynomial solutions of linear elliptic equations with constant coefficients in the complex plane

2020 ◽  
Vol 17 (4) ◽  
pp. 594-600
Author(s):  
Olga Trofymenko
Keyword(s):  
Elliptic Equation ◽  
Complex Plane ◽  
Elliptic Equations ◽  
Regular Polygon ◽  
Mean Value ◽  
Linear Elliptic Equation ◽  
Mean Value Theorems ◽  
Polynomial Solutions ◽  
Constant Coefficients ◽  
The Mean

We characterize solutions of the mean value linear elliptic equation with constant coefficients in the complex plane in the case of regular polygon.

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