Gehring theory for time-discrete hyperbolic differential equations
Hoshino, Keisuke ; Kikuchi, Norio
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998), p. 697-707 / Harvested from Czech Digital Mathematics Library

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

Publié le : 1998-01-01
Classification:  26D15,  35L20,  35L90,  39A10,  49J40
@article{119045,
     author = {Keisuke Hoshino and Norio Kikuchi},
     title = {Gehring theory for time-discrete hyperbolic differential equations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {39},
     year = {1998},
     pages = {697-707},
     zbl = {1060.35527},
     mrnumber = {1715459},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119045}
}
Hoshino, Keisuke; Kikuchi, Norio. Gehring theory for time-discrete hyperbolic differential equations. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 697-707. http://gdmltest.u-ga.fr/item/119045/

Calderón A.P.; Zygmund A. On the existence of certain singular integrals, Acta Math. 88 (1952), 85-139. (1952) | MR 0052553

Gehring F.W. The $L^p$-integrability of the partial derivatives of a quasi conformal mapping, Acta Math. 130 (1973), 265-277. (1973) | MR 0402038 | Zbl 0258.30022

Giaquinta M. Multiple integrals in the calculus of variations and non linear elliptic systems, Vorlesungsreihe des Sonderforschungsbereiches, Universität Bonn, 1981. | Zbl 0498.49001

Giaquinta M. Introduction to regularity theory for nonlinear elliptic systems, Lecture in Mathematics, Birkhäuser, 1993. | MR 1239172 | Zbl 0786.35001

Giaquinta M.; Giusti E. Partial regularity for the solutions to nonlinear parabolic systems, Ann. Mat. Pura Appl. 47 (1973), 253-266. (1973) | MR 0338568 | Zbl 0276.35062

Giaquinta M.; Giusti E. On the regularity of the minima of variational integrals, Acta Math. 148 (1982), 31-46. (1982) | MR 0666107 | Zbl 0494.49031

Giaquinta M.; Modica G. Regularity results for some classes of higher order non linear elliptic systems, J. Reine Angew. Math. 311/312 (1979), 145-169. (1979) | MR 0549962 | Zbl 0409.35015

Giaquinta M.; Struwe M. On the partial regularity of weak solutions of non-linear parabolic systems, Math. Z. 142 (1982), 437-451. (1982)

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) | MR 1629761

Haga J.; Kikuchi N. On the higher integrability of gradients of the solutions to difference partial differential systems of elliptic-parabolic type, preprint.

Hoshino K. On a method constructing solutions to hyperbolic partial differential equations, Nonlinear Studies 4 (1997), 133-142. (1997) | MR 1485185 | Zbl 0909.35083

Hoshino K. On a construction of weak solutions to semilinear dissipative hyperbolic systems with the higher integrable gradients, to appear in Nonlinear Analysis. | MR 1710157 | Zbl 0941.35044

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) | MR 1699114

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. | MR 1178095 | Zbl 0850.76043

Kikuchi N. A construction method of Morse flows to variational functionals, Nonlinear World 1 (1994), 131-147. (1994) | MR 1297075

Rothe E. Wärmeleitungsgleichung mit nichtkostanten Koeffizienten, Math. Ann. 104 (1931), 340-362. (1931) | MR 1512671

Stein E.M. Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, 1970. | MR 0290095 | Zbl 0281.44003