A criterion for uniform approximability of individual functions by solutions of second-order homogeneous elliptic equations with constant complex coefficients

2020 ◽  
Vol 211 (9) ◽  
pp. 1267-1309
Author(s):  
M. Ya. Mazalov
Keyword(s):  
Elliptic Equations ◽  
Second Order ◽  
Complex Coefficients ◽  
Constant Complex

Approximation on Closed Sets by Analytic or Meromorphic Solutions of Elliptic Equations and Applications

2002 ◽  
Vol 54 (5) ◽  
pp. 945-969 ◽  
Author(s):  
André Boivin ◽  
Paul M. Gauthier ◽  
Petr V. Paramonov
Keyword(s):  
Elliptic Equations ◽  
Partial Differential Operator ◽  
Elliptic Partial Differential Equations ◽  
Meromorphic Solutions ◽  
Partial Differential ◽  
Closed Sets ◽  
Carleman Type ◽  
Complex Coefficients ◽  
Constant Complex ◽  
Class Of Functions

AbstractGiven a homogeneous elliptic partial differential operator L with constant complex coefficients and a class of functions (jet-distributions) which are defined on a (relatively) closed subset of a domain Ω in Rn and which belong locally to a Banach space V, we consider the problem of approximating in the norm of V the functions in this class by “analytic” and “meromorphic” solutions of the equation Lu = 0. We establish new Roth, Arakelyan (including tangential) and Carleman type theorems for a large class of Banach spaces V and operators L. Important applications to boundary value problems of solutions of homogeneous elliptic partial differential equations are obtained, including the solution of a generalized Dirichlet problem.

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