Masashi Misawa
Existence of a classical solution for linear parabolic systems of nondivergence form

Comment.Math.Univ.Carolinae 45,3 (2004) 475-482.

Abstract: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.

Keywords: linear parabolic system, nondivergence, nondiagonal form, $L^{\infty }$-estimate, \newline Schauder estimate
AMS Subject Classification: 35B45, 35K40, 45, 50