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Polichka, A. E.; Tiunchik, M. F.

\(L_p\)-estimates for the solutions of a finite-difference boundary-value problem. (English) Zbl 0505.34047

Sib. Math. J. 22, 929-934 (1982).
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MSC:

34G10 Linear differential equations in abstract spaces
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K30 Functional-differential equations in abstract spaces
47B39 Linear difference operators
47E05 General theory of ordinary differential operators

Keywords:

corrected solvability; coercive operator; Hilbert space

Citations:

Zbl 0492.34049
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Full Text: DOI

References:

[1] S. G. Krein, Linear Differential Equations in Banach Space, Am. Math. Soc., Providence (1971). · Zbl 0236.47034
[2] A. E. Polichka and P. E. Sobolevskii, ?Estimates of the solutions of a difference boundary-value problem in the norm of the space of ?traces? of solutions of differential problems,? Tr. NIIM VGU, Voronezh, No. 19, 108-122 (1975).
[3] A. E. Polichka and P. E. Sobolevskii, ?The correct solvability of a difference boundary-value problem in a Bochner space,? Ukr. Mat. Zh.,28, No. 4, 511-523 (1976).
[4] A. E. Polichka and P. E. Sobolevskii, ?New Lp-estimates for parabolic difference problems,? Zh. Vychisl. Mat. Mat. Fiz.,16, No. 5, 1155-1163 (1976). · Zbl 0359.35068
[5] E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Am. Math. Soc., Providence (1957). · Zbl 0078.10004
[6] A. Benedek, A. P. Calderon, and R. Panzone, ?Convolution operators on Banach space valued functions,? Proc. Nat. Acad. Sci. USA,48, No. 3, 356-365 (1962). · Zbl 0103.33402 · doi:10.1073/pnas.48.3.356
[7] G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press (1959).
[8] V. G. Maz’ya and P. E. Sobolevskii, ?On generating operators of semigroups,? Usp. Mat. Nauk,17, No. 6, 151-154 (1962).
[9] O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968).
[10] S. Agmon, A. Douglis, and L. Nirenberg, ?Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions,? Commun. Pure Appl. Math., I:12, No. 4, 623-727 (1959); II;17, No. 1, 35-92 (1964). · Zbl 0093.10401 · doi:10.1002/cpa.3160120405
[11] M. Z. Solomyak, ?The analyticity of semigroups generated by an elliptic operator in the spaces Lp,? Dokl. Akad. Nauk SSSR,127, No. 1, 37-39 (1959). · Zbl 0087.11703
[12] A. A. Samarskii, Introduction to the Theory of Finite Difference Schemes [in Russian], Nauka, Moscow (1971).
[13] P. E. Sobolevskii and M. F. Tiunchik, ?On the difference method for the approximate solution of boundary value problems for quasilinear elliptic and parabolic equations,? Tr. Mat. Inst. Voronezh. Gos. Univ., No. 1, 82-106 (1970).
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