Geodesic
Proof of Schauder estimates for parabolic initial-boundary value model problems via O. A. Ladyzhenskaya's Fourier multipliers theorem
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Tome 444 (2016), pp. 133-156 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is concerned with estimates of the Hölder norms of solutions of model parabolic initial-boundary value problems in a half-space. The proof is based on the theorem on the Fourier multipliers in anisotropic Hölder spaces due to O. A. Ladyzhenskaya and on K. K. Golovkin's theorem on equivalent norms in these spaces. 
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V. A. Solonnikov. Proof of Schauder estimates for parabolic initial-boundary value model problems via O. A. Ladyzhenskaya's Fourier multipliers theorem. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Tome 444 (2016), pp. 133-156. http://geodesic.mathdoc.fr/item/ZNSL_2016_444_a7/

[1] O. A. Ladyzhenskaya, “A theorem of multiplicators in non-homogeneous Hölder spaces and some of its applications”, Zap. Nauchn. Semin. POMI, 271, 2000, 156–174 | MR | Zbl

[2] O. A. Ladyzhenskaya, G. A. Seregin, “Coercive estimate for solutions to the linearizations of the modified Navier–Stokes equations”, Doklady RAN, 370:6 (2000), 738–740 | MR | Zbl

[3] L. Hörmander, The analysis of linear partial differential operators, v. 1, Grund. Mathem. Wissen., 256, 1983 | MR | Zbl

[4] K. K. Golovkin, V. A. Solonnikov, “On some estimates of convolutions”, Zap. Nauchn. Semin. LOMI, 7, 1968, 6–86 | MR | Zbl

[5] N. K. Bary, Trigonometric series, Fizmatgiz, Moscow, 1961

[6] V. A. Solonnikov, “On boundary value problems for linear parabolic systems of differential equations of a general form”, Tr. MIAN, 83, 1965, 3–163 | MR | Zbl

[7] K. K. Golovkin, “On the equivalent norms in fractional spaces”, Tr. MIAN, 66, 1962, 364–383 | MR | Zbl

[8] K. K. Golovkin, “On conditions of smoothness of functions of several variables and on the estimate of convolution operators”, Doklady AN SSSR, 139:3 (1961), 524–537 | MR

[9] V. A. Solonnikov, “Estimates of solutions of a non-stationary linearized Navier–Stokes system of equations”, Tr. MIAN, 70, 1964, 213–317 | MR | Zbl

[10] O. A. Ladyzhenskaya, “On the uniqueness of the solution of the Cauchy problem for a linear parabolic equation”, Matem. Sbornik, 27(69):2 (1950), 175–184 | MR | Zbl

[11] S. Agmon, A. Douglis, L. Nirenberg, “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I”, Comm. Pure. Appl. Math., 12 (1959), 628–727 | DOI | MR

[12] M. Z. Solomiak, “Evaluation of norm of the resolvent of elliptic operators in $L_p$-spaces”, Uspekhi Mat. Nauk, 15:6 (1960), 141–148 | MR | Zbl

[13] M. S. Agranovich, M. I. Vishik, “Elliptic parameter dependent problems and parabolic problems of general form”, Uspekhi Matem. Nauk, 19:3 (1964), 53–161 | MR | Zbl

[14] S. D. Eidelman, Parabolic systems, Nauka, Moscow, 1964 | MR