Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 29, Tome 249 (1997), pp. 20-39
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A. A. Arkhipova. On the partial regularity up to the boundary of weak solutions to quasilinear parabolic systems with quadratic growth. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 29, Tome 249 (1997), pp. 20-39. http://geodesic.mathdoc.fr/item/ZNSL_1997_249_a1/
@article{ZNSL_1997_249_a1,
author = {A. A. Arkhipova},
title = {On~the partial regularity up to the boundary of weak solutions to quasilinear parabolic systems with quadratic growth},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {20--39},
year = {1997},
volume = {249},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_249_a1/}
}
TY - JOUR
AU - A. A. Arkhipova
TI - On the partial regularity up to the boundary of weak solutions to quasilinear parabolic systems with quadratic growth
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1997
SP - 20
EP - 39
VL - 249
UR - http://geodesic.mathdoc.fr/item/ZNSL_1997_249_a1/
LA - en
ID - ZNSL_1997_249_a1
ER -
%0 Journal Article
%A A. A. Arkhipova
%T On the partial regularity up to the boundary of weak solutions to quasilinear parabolic systems with quadratic growth
%J Zapiski Nauchnykh Seminarov POMI
%D 1997
%P 20-39
%V 249
%U http://geodesic.mathdoc.fr/item/ZNSL_1997_249_a1/
%G en
%F ZNSL_1997_249_a1
We consider quasilinear nondiagonal parabolic systems with quadratic growth on the gradient in a parabolic cylinder $Q$. Under Dirichlet and Neumann boundary conditions partial Hölder continuity up to the lateral surface of $Q$ of solutions $u\in W_2^{1,1} (Q)\cap L^\infty(Q)$ is proved. Hausdorff dimension of a singular set is estimated. In the proof we get of the maximum principle theorem for corresponding model linear problems.
