Approximation on Closed Sets by Analytic or Meromorphic Solutions of Elliptic Equations and Applications
2002 ◽
Vol 54
(5)
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pp. 945-969
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Keyword(s):
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.
1986 ◽
Vol 6
(2-4)
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pp. 235-247
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1996 ◽
Vol 187
(3)
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pp. 385-402
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1996 ◽
Vol 119
(2)
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pp. 363-371
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2009 ◽
1966 ◽
Vol 20
(1)
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pp. 56-60
2015 ◽
Vol 53
(1)
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pp. 405-420
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1976 ◽
Vol 10
(3)
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pp. 527-533
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2012 ◽
Vol 252
(3)
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pp. 2266-2295
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2001 ◽
Vol 13
(5)
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pp. 327-350
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