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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am35-1-4,
author = {Dmitry Portnyagin},
title = {Full regularity of bounded solutions to nondiagonal parabolic systems of two equations},
journal = {Applicationes Mathematicae},
volume = {35},
year = {2008},
pages = {69-79},
zbl = {1146.35328},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am35-1-4}
}
Dmitry Portnyagin. Full regularity of bounded solutions to nondiagonal parabolic systems of two equations. Applicationes Mathematicae, Tome 35 (2008) pp. 69-79. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am35-1-4/