In this paper, a "matching" method for planar harmonic functions is exhibited, using an elliptic adjoint equation L*u = 0.The harmonic functions considered, here, are considered to be periodic in the variable y and their product is assumed to be positive. Actually, some suitable compatibility conditions must be verified. Our "gluing" result is obtained by means of a matching procedure for elliptic equations that goes back to M.V. Safonov.
A gluing theorem for the elliptic adjoint operator L* in the plane / O. Arena. - In: BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. B. - ISSN 0392-4041. - STAMPA. - 9:(2009), pp. 1-6.
A gluing theorem for the elliptic adjoint operator L* in the plane
ARENA, ORAZIO
2009
Abstract
In this paper, a "matching" method for planar harmonic functions is exhibited, using an elliptic adjoint equation L*u = 0.The harmonic functions considered, here, are considered to be periodic in the variable y and their product is assumed to be positive. Actually, some suitable compatibility conditions must be verified. Our "gluing" result is obtained by means of a matching procedure for elliptic equations that goes back to M.V. Safonov.
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