On the analyticity of the solutions of evolutionary equations generated by elliptic operators perturbations

A.O. Lopushansky

Was generalize a theorem of S.Agmon on analytic continuation from the theory of evolutionary equations, generated by elliptic operators, onto classes of perturbed operators, is reduced. The perturbation is described by interpolation of domain of definition of the given elliptic operator and input space.

1. Tanabe H. Equations of evolution , Pitman – 1979

2. Agmon S. On the eigenfunctions and on the eigenvalues of elliptic boundary value problems // Comm. Pure Appl. Math. – 1962 V. 15 p. 119–147

3. Grisvard P Équations operationnelles abstraites et problémes aux limites dans des domaines non réguliers // Actes. Congrés Intern. Math., 1970. – 1971 V. 2 p. 731–736

4. Bergh J., Löfström J. Interpolation spaces , Springer – 1978

5. Лопатинский Я.Б. Об одном способе приведения граничных задач для системы дифференциальных уравнений эллиптического типа к регулярным интегральным уравнениям // Укр. мат. журн. – 1953 V. 5 p. 123–151

	On the analyticity of the solutions of evolutionary equations generated by elliptic operators perturbations
Author	A.O. Lopushansky State University “Lviv Politechnics”
Abstract	Was generalize a theorem of S.Agmon on analytic continuation from the theory of evolutionary equations, generated by elliptic operators, onto classes of perturbed operators, is reduced. The perturbation is described by interpolation of domain of definition of the given elliptic operator and input space.
Keywords	Agmon theorem, analytic continuation, evolutionary equations, elliptic operators, perturbed operators, domain interpolation, input space
DOI	doi:10.30970/ms.12.2.145-148
Reference	1. Tanabe H. Equations of evolution , Pitman – 1979 2. Agmon S. On the eigenfunctions and on the eigenvalues of elliptic boundary value problems // Comm. Pure Appl. Math. – 1962 V. 15 p. 119–147 3. Grisvard P Équations operationnelles abstraites et problémes aux limites dans des domaines non réguliers // Actes. Congrés Intern. Math., 1970. – 1971 V. 2 p. 731–736 4. Bergh J., Löfström J. Interpolation spaces , Springer – 1978 5. Лопатинский Я.Б. Об одном способе приведения граничных задач для системы дифференциальных уравнений эллиптического типа к регулярным интегральным уравнениям // Укр. мат. журн. – 1953 V. 5 p. 123–151
Pages	145-148
Volume	12
Issue	2
Year	1999
Journal	Matematychni Studii
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