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.
Hölder continuity of weak solutions is studied for a nondiagonal parabolic system of singular quasilinear differential equations with matrix of coefficients satisfying special structure conditions. A technique based on estimating linear combinations of the unknowns is employed.
-estimates of weak solutions are established for a quasilinear non-diagonal parabolic system with a special structure whose leading terms are modelled by p-Laplacians. A generalization of the weak maximum principle to systems of equations is employed.
A generalization of the well-known weak maximum principle is established for a class of quasilinear strongly coupled parabolic systems with leading terms of p-Laplacian type.
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