Geodesic
Existence of a classical solution for linear parabolic systems of nondivergence form
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 3, pp. 475-482

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We prove the unique existence of a classical solution for a linear parabolic system of nondivergence and nondiagonal form. The key ingredient is to combine the energy estimates with Schauder estimates and to obtain a uniform boundedness of a solution.
Classification : 35A05, 35B45, 35D10, 35K40, 35K50
Keywords: linear parabolic system; nondivergence; nondiagonal form; $L^{\infty }$-estimate; \newline Schauder estimate 
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     title = {Existence of a classical solution for linear parabolic systems of nondivergence form},
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Misawa, Masashi. Existence of a classical solution for linear parabolic systems of nondivergence form. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 3, pp. 475-482. http://geodesic.mathdoc.fr/item/CMUC_2004__45_3_a7/