Full regularity of bounded solutions to nondiagonal parabolic systems of two equations

Volume 35 / 2008

Dmitry Portnyagin Applicationes Mathematicae 35 (2008), 69-79 MSC: Primary 35B50; Secondary 35K40, 35K55. DOI: 10.4064/am35-1-4


Hölder continuity and, basing on this, full regularity and global existence of weak solutions is studied for a general nondiagonal parabolic system of nonlinear differential equations with the matrix of coefficients satisfying special structure conditions and depending on the unknowns. A technique based on estimating a certain function of unknowns is employed to this end.


  • Dmitry PortnyaginInstitute for Condensed Matter Physics
    National Academy of Sciences of Ukraine
    1 Svientsitskii Street, 79011 Lviv, Ukraine

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