-regularity results for quasilinear parabolic systems
Alain Bensoussan, Jens Frehse (1990)
Commentationes Mathematicae Universitatis Carolinae
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Alain Bensoussan, Jens Frehse (1990)
Commentationes Mathematicae Universitatis Carolinae
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Masashi Misawa (2004)
Commentationes Mathematicae Universitatis Carolinae
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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.
Michael Struwe (1984)
Czechoslovak Mathematical Journal
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Arina A. Arkhipova, Jana Stará (2010)
Commentationes Mathematicae Universitatis Carolinae
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We derive local a priori estimates of the Hölder norm of solutions to quasilinear elliptic systems with quadratic nonlinearities in the gradient. We assume higher integrability of solutions and smallness of its BMO norm but the Hölder norm is estimated in terms of BMO norm of the solution under consideration, only.