Asymptotic expansion of singular operators on Sobolev spaces

Article type: Research Article

Authors: Penzel, F.^{; ;} | Speck, F.-O.

Affiliations: Fachbereich Mathematik, Technische Hochschule Darmstadt, Darmstadt, Germany | Departamento de Matemática, Instituto Superior Técnico, Lisboa, Portugal

Note: [] Correspondence to: F. Penzel, Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany.

Note: [] Supported by an INIDA project of Deutscher Akademischer Austauschdienst and Instituto Nacional de Investigação Científica.

Abstract: The topic of asymptotic expansion of solutions of pseudodifferential equations in the spirit of Eskin's work is extended to a more general situation. Taylor expansion of Fourier symbol matrix functions is replaced by a series of generalized invertible operators, which act on vector Sobolev spaces. The fractional orders of these spaces are obtained from the jumps of the lifted symbol matrix at infinity in a situation which is most interesting for applications. Asymptotic and regularity results for the solutions of corresponding systems of equations are direct consequences.

DOI: 10.3233/ASY-1993-7404

Journal: Asymptotic Analysis, vol. 7, no. 4, pp. 287-300, 1993