Abstract
We present sufficient conditions for the existence of solutions of general boundary-value problems in a half-space for inhomogeneous differential equations with constant coefficients and arbitrary boundary data in the space of tempered distributions.
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References
S. Agmon, A. Douglis, and L. Nirenberg, “Estimates near the boundary for solutions to elliptic partial differential equations satisfying general boundary conditions I.,” Comm. Pure Appl. Math., 12, 623—727 (1959).
G. V. Dikopolov and G. E. Shilov, “On the well-defined boundary-value problems for partial differential equations in a half-space,” Izv. AN SSSR. Ser. Mat., 24, 369–380 (1960).
G. V. Dikopolov and G. E. Shilov, “On the well-defined boundary-value problems in a half-space for partial differential equations with right-hand side,” Sib. Mat. Zh., 1, No. 1, 45–61 (1960).
S. K. Godunov, Ordinary Differential Equations with Constant Coefficients. Vol. 1: Boundary-value problems [in Russian], Novosibirsk Univ., Novosibirsk, 1994.
V. P. Palamodov, “On the well-defined boundary-value problems for partial differential equations in a half-space,” Izv. AN SSSR. Ser. Mat., 24, 381–386 (1960).
G. V. Dikopolov, “On boundary-value problems for differential equations with constant coefficients in a half-space,” Matem. Sb., 59(101), 215–228 (1962).
A. L. Pavlov, “On general boundary-value problems for differential equations with constant coefficients in a half-space,” Matem. Sb., 103(145), No. 3(7), 367–391 (1977).
A. L. Pavlov, “The well-posedness of general boundary-value problems in a half-space for differential equations with constant coefficients in the classes of functions of power growth and decrease,” Ukr. Mat. Vest., 7, No. 1, 73–118 (2010).
A. L. Pavlov, “The solvability of boundary-value problems in a half-space for differential equations with constant coefficients in a class of tempered distributions,” Sib. Mat. Zh., 54, No. 4, 871–889 (2013).
N. E. Tovmasyan, “The well-posedness of boundary-value problems for partial differential equations in a half-space in a class of distributions,” Sib. Mat. Zh., 28, No. 2, 171–185 (1987).
L. R. Volevich and S. G. Gindikin, “The Cauchy problem and related problems for equations in convolutions,” Uspekhi Mat. Nauk, 72, No. 3, 65–143 (1972).
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 10, No. 3, pp. 360–378, July–August, 2013.
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Pavlov, A.L. Solvability of general boundary-value problems in a half-space for inhomogeneous differential equations with constant coefficients. J Math Sci 196, 665–678 (2014). https://doi.org/10.1007/s10958-014-1684-7
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DOI: https://doi.org/10.1007/s10958-014-1684-7