Abstract
Necessary and sufficient conditions are found under which the classical solutions of 2\(\overrightarrow b\)-parabolic systems, defined in a halfopen layer, can be represented as the Poisson integrals of functions or generalized Borel measures from the special spaces Lp k(0,a), 1 < p ≤ ∞, or Mk(0,a). It is elucidated as to in what sense the solutions, representable by Poisson integrals, satsfy the initial conditions.
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S. D. Éidel'man, Parabolic Systems [in Russian], Nauka, Moscow (1964).
S. D. Ivasishen and S. D. Éidel'man, “The 2\(\overrightarrow b\)-parabolic systems,” in: Proceedings of the Seminar on Functional Analysis [in Russian], No. 1, Inst. Mat. Akad. Nauk UkrSSR, Kiev (1968), pp. 3–175.
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S. D. Ivasishen, “On integral representations and Fatou's property for solutions of parabolic systems,” Usp. Mat. Nauk,41, No. 4, 173–174 (1986).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 500–506, April, 1990.
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Ivasishen, S.D. Integral representation and initial values of solutions of 2\(\overrightarrow b\)-parabolic systems. Ukr Math J 42, 443–448 (1990). https://doi.org/10.1007/BF01071332
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DOI: https://doi.org/10.1007/BF01071332