Existence of a classical solution for linear parabolic systems of nondivergence form

Masashi Misawa

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 3, page 475-482
  • ISSN: 0010-2628

Abstract

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We prove the unique existence of a classical solution for a linear parabolic system of nondivergence and nondiagonal form. The key ingredient is to combine the energy estimates with Schauder estimates and to obtain a uniform boundedness of a solution.

How to cite

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Misawa, Masashi. "Existence of a classical solution for linear parabolic systems of nondivergence form." Commentationes Mathematicae Universitatis Carolinae 45.3 (2004): 475-482. <http://eudml.org/doc/249376>.

@article{Misawa2004,
abstract = {We prove the unique existence of a classical solution for a linear parabolic system of nondivergence and nondiagonal form. The key ingredient is to combine the energy estimates with Schauder estimates and to obtain a uniform boundedness of a solution.},
author = {Misawa, Masashi},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {linear parabolic system; nondivergence; nondiagonal form; $L^\{\infty \}$-estimate; Schauder estimate; linear parabolic systems; nondivergence form; classical solutions; Schauder estimates; gradient flows; -harmonic maps},
language = {eng},
number = {3},
pages = {475-482},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Existence of a classical solution for linear parabolic systems of nondivergence form},
url = {http://eudml.org/doc/249376},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Misawa, Masashi
TI - Existence of a classical solution for linear parabolic systems of nondivergence form
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 3
SP - 475
EP - 482
AB - We prove the unique existence of a classical solution for a linear parabolic system of nondivergence and nondiagonal form. The key ingredient is to combine the energy estimates with Schauder estimates and to obtain a uniform boundedness of a solution.
LA - eng
KW - linear parabolic system; nondivergence; nondiagonal form; $L^{\infty }$-estimate; Schauder estimate; linear parabolic systems; nondivergence form; classical solutions; Schauder estimates; gradient flows; -harmonic maps
UR - http://eudml.org/doc/249376
ER -

References

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  1. Campanato S., Equazioni paraboliche del secondo ordine e spazi ℒ 2 , θ ( Ø m e g a , δ ) , Ann. Mat. Pura Appl. (4) 73 (1966), 55-102. (1966) MR0213737
  2. Giaquinta M., Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Mathematics Studies {105}, Princeton Univ. Press, Princeton, NJ, 1983. Zbl0516.49003MR0717034
  3. Giaquinta M., Introduction to Regularity Theory for Nonlinear Elliptic Systems, Birkhäuser Verlag, Basel, 1993. Zbl0786.35001MR1239172
  4. Giaquinta M., Struwe M., On the regularity of weak solutions of nonlinear parabolic systems, Math. Z. 179 (1982), 437-451. (1982) MR0652852
  5. Misawa M., Existence and regularity results for the gradient flow for p -harmonic maps, Electron. J. Diff. Equations 1998 (1998), 36 1-17. (1998) Zbl0948.58013MR1658020
  6. Schlag W., Schauder and L p estimates for parabolic systems via Campanato spaces, Comm. Partial Differential Equations 21 7-8 (1996), 1141-1175. (1996) MR1399194
  7. Struwe M., Some regularity results for quasilinear parabolic systems, Comment. Math. Univ. Carolinae 26 (1985), 129-150. (1985) MR0797297

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