Gehring theory for time-discrete hyperbolic differential equations

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1. Calderón A.P., Zygmund A., On the existence of certain singular integrals, Acta Math. 88 (1952), 85-139. (1952) MR0052553
2. Gehring F.W., The $L^p$-integrability of the partial derivatives of a quasi conformal mapping, Acta Math. 130 (1973), 265-277. (1973) Zbl0258.30022MR0402038
3. Giaquinta M., Multiple integrals in the calculus of variations and non linear elliptic systems, Vorlesungsreihe des Sonderforschungsbereiches, Universität Bonn, 1981. Zbl0498.49001
4. Giaquinta M., Introduction to regularity theory for nonlinear elliptic systems, Lecture in Mathematics, Birkhäuser, 1993. Zbl0786.35001MR1239172
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
6. Giaquinta M., Giusti E., On the regularity of the minima of variational integrals, Acta Math. 148 (1982), 31-46. (1982) Zbl0494.49031MR0666107
7. 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) Zbl0409.35015MR0549962
8. Giaquinta M., Struwe M., On the partial regularity of weak solutions of non-linear parabolic systems, Math. Z. 142 (1982), 437-451. (1982) 
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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