References
- Kamynin LI. Gevrey's theory for parabolic potentials: VI. Differ Equ. 1972;8(6):770–778.
- Kamynin LI. Applications of parabolic Pagni potentials to boundary value problems in mathematical physics. I. Differ Equ. 1990;26(5):596–606.
- Kamynin LI. Applications of parabolic Pagni potentials to boundary value problems in mathematical physics. II. Differ Equ. 1991;27(2):250–263.
- Baderko EA. Parabolic problems and boundary integral equations. Math Methods Appl Sci. 1997;20:449–459.
- Konenkov AN. The first boundary value problem for a parabolic equation in the Hölder class Hα. Differ Equ. 2004;40(3):420–427.
- Cherepova MF. On the solvability of boundary value problems for a parabolic equation with coefficients growing near the boundary. Differ Equ. 2007;43(1):118–129.
- Konenkov AN. Solutions of model heat problems in Zygmund spaces. Differ Equ. 2008;44(10):1448–1459.
- Konenkov AN. Boundary value problems for parabolic equations in Zygmund spaces. Doklady Math. 2008;77(1):9–12.
- Konenkov AN. Solvability of a model oblique derivative problem for the heat equation in the Zygmund space H1. Differ Equ. 2018;54(5):658–668.
- Baderko EA. On solution by the method of potentials of a heat problem with concentrated heat capacities. Differ Uravn. 1972;8(7):1225–1234. Russian.
- Kamynin LI. On solution of the fundamental boundary value problems for a one-dimensional parabolic equation of second order by the method of potentials. Sib Math J. 1974;15(4):573–592.
- Zeineddin M. On a single layer potential for a parabolic system in the Dini classes [dissertation]. Moscow (Russian); 1992.
- Baderko EA, Cherepova MF. Simple layer potential and the first boundary value problem for a parabolic system on the plane. Differ Equ. 2016;52(2):197–209.
- Baderko EA, Cherepova MF. Dirichlet problem for parabolic systems with Dini continuous coefficients on the plane. Doklady Math. 2017;96(2):423–426.
- Maz'ya VG, Kresin GI. On the maximum principle for strongly elliptic and parabolic second order systems with constant coefficients. Math USSR Sb. 1986;53(2):457–479.
- Petrovskii IG. On the Cauchy problem for systems of linear partial differential equations in domain of nonanalytic functions. Bull Moskov Gos Univ Sekts A. 1938;1(7):1–72.
- Dzyadyk VK. Introduction to the theory of uniform approximation of functions by polynomials. Moscow: Nauka; 1977.
- Zeineddin M. Smoothness of a Single Layer Potential for a Parabolic System of the Second Order in the Dini Classes. Deposited in VINITI. 16.04.92; 1294–B92. Russian.
- Eidel'man SD, Ivasyshen SD, Kochubey AN. Analytic methods in the theory of differential and pseudo-differential equations of parabolic type. Basel, Boston, Berlin: Birkhäuser; 2004.
- Friedman A. Partial differential equations of parabolic type. New York (NY): Dover Publ.; 2008.
- Arnol'd VI. Obyknovennye differentsial'nye uravneniya [Ordinary Differential Equations]. Moscow: Nauka; 1984.
- Kamynin LI. The smoothness of thermal potentials in Dini-Hölder space. Sib Math J. 1971;11(5):757–776.
- Baderko EA, Cherepova MF. Bitsadze-Samarskii problem for parabolic systems with Dini continuous coefficients. Complex Var Elliptic Equ. 2019;64(5):753–765.
- Tikhonov AN. On functional equations of the Volterra type and their applications to some problems of mathematical physics. Bull Moskov Gos Univ Sekts A. 1938;1(8):1–25.
- Semaan KhM. On the solution of the second boundary value problem for parabolic systems on the plane [dissertation]. Moscow (Russian); 1999.
- Piskorek A. ‘E tude de la continuit'e reguli‘ere d'une int'egrale concernant la d'erivee transversale relative ‘a un syst‘eme parabolique. Ann Polon Math. 1964;15(3):289–301.
- Tveritinov VA. Smoothness of the Single Layer Potential for Second Order Parabolic Systems. Deposited in VINITI. 02.09.88; 6850–V88. Russian.
- Baderko EA, Cherepova MF. Smoothness in the Dini space of a single layer potential for a parabolic system in the plane. J Math Sci. 2018;235(2):154–167.