Gehring theory for time-discrete hyperbolic differential equations

Keisuke Hoshino; Norio Kikuchi

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 4, page 697-707
  • ISSN: 0010-2628

Abstract

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This paper is concerned with extending Gehring theory to be applicable to Rothe's approximate solutions to hyperbolic differential equations.

How to cite

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Hoshino, Keisuke, and Kikuchi, Norio. "Gehring theory for time-discrete hyperbolic differential equations." Commentationes Mathematicae Universitatis Carolinae 39.4 (1998): 697-707. <http://eudml.org/doc/248259>.

@article{Hoshino1998,
abstract = {This paper is concerned with extending Gehring theory to be applicable to Rothe's approximate solutions to hyperbolic differential equations.},
author = {Hoshino, Keisuke, Kikuchi, Norio},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Gehring theory; Rothe's approximation; hyperbolic differential equations; higher integrability; Gehring's lemma; hyperbolic differential equations; covering theorems},
language = {eng},
number = {4},
pages = {697-707},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Gehring theory for time-discrete hyperbolic differential equations},
url = {http://eudml.org/doc/248259},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Hoshino, Keisuke
AU - Kikuchi, Norio
TI - Gehring theory for time-discrete hyperbolic differential equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 4
SP - 697
EP - 707
AB - This paper is concerned with extending Gehring theory to be applicable to Rothe's approximate solutions to hyperbolic differential equations.
LA - eng
KW - Gehring theory; Rothe's approximation; hyperbolic differential equations; higher integrability; Gehring's lemma; hyperbolic differential equations; covering theorems
UR - http://eudml.org/doc/248259
ER -

References

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  5. Giaquinta M., Giusti E., Partial regularity for the solutions to nonlinear parabolic systems, Ann. Mat. Pura Appl. 47 (1973), 253-266. (1973) Zbl0276.35062MR0338568
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  9. Haga J., Kikuchi N., On the existence of the harmonic variational flow subject to the two-sided conditions, Zap. Nauch. Semi. POMI. 243 (1997), 324-337. (1997) MR1629761
  10. Haga J., Kikuchi N., On the higher integrability of gradients of the solutions to difference partial differential systems of elliptic-parabolic type, preprint. 
  11. Hoshino K., On a method constructing solutions to hyperbolic partial differential equations, Nonlinear Studies 4 (1997), 133-142. (1997) Zbl0909.35083MR1485185
  12. Hoshino K., On a construction of weak solutions to semilinear dissipative hyperbolic systems with the higher integrable gradients, to appear in Nonlinear Analysis. Zbl0941.35044MR1710157
  13. Hoshino K., Kikuchi N., On a construction of weak solutions to linear hyperbolic partial differential systems with the higher integrable gradients, Zap. Nauch. Semi. POMI. 233 (1996), 30-52. (1996) MR1699114
  14. Kikuchi N., An approach to the construction of Morse flows for variational functionals, in: Nematics-Mathematical and Physical Aspects, ed. by J.-M. Coron, J.-M. Ghidaglia and F. Helein, NATO Adv. Sci. Inst. Ser.C: Math. Phys. Sci. 332, Kluwer Acad. Publ., Dordrecht-Boston-London, 1991, pp.195-198. Zbl0850.76043MR1178095
  15. Kikuchi N., A construction method of Morse flows to variational functionals, Nonlinear World 1 (1994), 131-147. (1994) MR1297075
  16. Rothe E., Wärmeleitungsgleichung mit nichtkostanten Koeffizienten, Math. Ann. 104 (1931), 340-362. (1931) MR1512671
  17. Stein E.M., Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, 1970. Zbl0281.44003MR0290095

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