A priori estimates for quasilinear parabolic systems with quadratic nonlinearities in the gradient

Arina A. Arkhipova; Jana Stará

Commentationes Mathematicae Universitatis Carolinae (2010)

  • Volume: 51, Issue: 4, page 639-652
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Arkhipova, Arina A., and Stará, Jana. "A priori estimates for quasilinear parabolic systems with quadratic nonlinearities in the gradient." Commentationes Mathematicae Universitatis Carolinae 51.4 (2010): 639-652. <http://eudml.org/doc/246945>.

@article{Arkhipova2010,
abstract = {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.},
author = {Arkhipova, Arina A., Stará, Jana},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quasilinear parabolic systems; quadratic nonlinearities; regularity; Morrey; VMO spaces; quasilinear parabolic system; quadratic nonlinearity; regularity; Morrey; VMO space},
language = {eng},
number = {4},
pages = {639-652},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A priori estimates for quasilinear parabolic systems with quadratic nonlinearities in the gradient},
url = {http://eudml.org/doc/246945},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Arkhipova, Arina A.
AU - Stará, Jana
TI - A priori estimates for quasilinear parabolic systems with quadratic nonlinearities in the gradient
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 4
SP - 639
EP - 652
AB - 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.
LA - eng
KW - quasilinear parabolic systems; quadratic nonlinearities; regularity; Morrey; VMO spaces; quasilinear parabolic system; quadratic nonlinearity; regularity; Morrey; VMO space
UR - http://eudml.org/doc/246945
ER -

References

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