Laurent series for solutions of elliptic systems. (Ryad Lorana dlya reshenij ehllipticheskikh sistem).Ed. by M. A. Shubin. (Ryad Lorana dlya reshenij ehllipticheskikh sistem.) (Russian) Zbl 0743.35021

Tarkhanov, N. N.

Novosibirsk: Nauka. 317 p. (1991).

The monograph is devoted to local problems of the theory of linear PDE’s. Among the topics considered are removable singularities of systems of the equations, the expansion of solutions of elliptic systems into Laurent series (which is, actually, a discrete representation of the corresponding Green’s function), uniform approximations and approximations on average for the solutions, solvability conditions for the Cauchy problem for elliptic systems, etc. The results presented in the book are obtained by means of complex analysis technique.

Reviewer: B.A.Malomed (Ramat Aviv)

MSC:

35J45	Systems of elliptic equations, general (MSC2000)
35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations
34C10	Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
30B10	Power series (including lacunary series) in one complex variable
35A35	Theoretical approximation in context of PDEs

Keywords:

removable singularities; Laurent series; Green’s function; Cauchy problem for elliptic systems