On the regularity of the weak solution of Cauchy problem for nonlinear parabolic systems via Liouville property

Oldřich John; Jana Stará

Commentationes Mathematicae Universitatis Carolinae (1984)

  • Volume: 025, Issue: 3, page 445-457
  • ISSN: 0010-2628

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John, Oldřich, and Stará, Jana. "On the regularity of the weak solution of Cauchy problem for nonlinear parabolic systems via Liouville property." Commentationes Mathematicae Universitatis Carolinae 025.3 (1984): 445-457. <http://eudml.org/doc/17336>.

@article{John1984,
author = {John, Oldřich, Stará, Jana},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {regularity; weak solution; Cauchy problem; nonlinear parabolic systems; Liouville property; quasilinear system; regularity up to the boundary},
language = {eng},
number = {3},
pages = {445-457},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the regularity of the weak solution of Cauchy problem for nonlinear parabolic systems via Liouville property},
url = {http://eudml.org/doc/17336},
volume = {025},
year = {1984},
}

TY - JOUR
AU - John, Oldřich
AU - Stará, Jana
TI - On the regularity of the weak solution of Cauchy problem for nonlinear parabolic systems via Liouville property
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1984
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 025
IS - 3
SP - 445
EP - 457
LA - eng
KW - regularity; weak solution; Cauchy problem; nonlinear parabolic systems; Liouville property; quasilinear system; regularity up to the boundary
UR - http://eudml.org/doc/17336
ER -

References

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  1. S. CAMPANATO, Partial Hölder continuity of solutions of quasilinear parabolic systems of second order with linear growth, Rend. Sem. Mat. Univ. Padova, Vol. 64 (1981), 60-75. (1981) Zbl0496.35012MR0636626
  2. M. GIAQUINTA E. GIUSTI, Partial regularity for the solutions to nonlinear parabolic systems, Annali di Matematica Pura ed Appl. 97 (1973), 253-266. (1973) MR0338568
  3. M. GIAQUINTA M. STRUWE, On the partial regularity of weak solutions of nonlinear parabolic systems, Math. Z. 179 (1982), 437-451. (1982) MR0652852
  4. M. STRUWE, A counterexample in regularity theory for parabolic systems, Czech. Math. Journal (to appear). Zbl0573.35053MR0743484
  5. M. GIAQUINTA J. NEČAS, On the regularity of weak solutions to nonlinear elliptic systems via Liouville's type property, Comment. Math. Univ. Carolinae 20 (1979), 111-121. (1979) MR0526152
  6. M. GIAQUINTA J. NEČAS, On the regularity of weak solutions to nonlinear elliptic systems of partial differential equations, J. reine angew. Math. 316 (1980), 140-159. (1980) MR0581329
  7. M. GIAQUINTA J. NEČAS O. JOHN J. STARÁ, On the regularity up to the boundary for second order nonlinear elliptic systems, Pacific J. of Math. 99 (1982), 1-17. (1982) MR0651482
  8. B. KAWOHL, On Liouville theorems, continuity and Hölder continuity of weak solution to some quasillnear elliptic systems, Comment. Math. Univ. Carolinae 21 (1980), 679-697. (1980) MR0597758
  9. S. HILDEBRANDT K. O. WIDMAN, Sätze von Liouvillesohen Typ für quasilineare elliptisohe Gleichungen und Systeme, Nach. Akad. Wiss. Göttingen, II. Math. Klasse, 4 (1979), 41-59. (1979) MR0568802
  10. M. MEIER, Liouville theorems for nonlinear elliptic equations and systems, Manuscripta Math. 29 (1979), 207-228. (1979) Zbl0426.35034MR0545042
  11. M. MEIER, Liouville theorems for nondiagonal elliptic systems in arbitrary dimensions, Math. Z. 176 (1981), 123-133. (1981) Zbl0454.35034MR0606175
  12. O. JOHN, The interior regularity and the Liouville property for the quasilinear parabolio systems, Comment. Math. Univ. Carolinae 13 (1982), 685-690. (1982) MR0687563

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