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A method for constructing solutions to linear systems of partial differential equations

Abstract

We obtain some conditions of solvability in Sobolev spaces for the systems of linear partial differential equations and deduce the corresponding formulas for solutions to these systems. The solutions are given as the sum of the series whose terms are the iterations of some pseudodifferential operators constructed explicitly.

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Dedicated to Yu. G. Reshetnyak on the occasion of his 75th birthday

Original Russian Text © A. A. Shlapunov, 2006, published in Matematicheskie Trudy, 2006, Vol. 9, No. 2, pp. 191–204.

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Shlapunov, A.A. A method for constructing solutions to linear systems of partial differential equations. Sib. Adv. Math. 17, 144–152 (2007). https://doi.org/10.3103/S1055134407020046

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Key words

  • overdetermined systems of partial differential equations
  • operator equations of the first kind