Literatur
Bellman, R.: Research Problem No. 15 (Generalized existence and uniqueness theorems). Bull. Am. Math. Soc.71, 709–710 (1965).
Bernstein, S. N.: Über beste Approximation stetiger Funktionen durch Polynome vorgegebenen Grades. Soobxč. Charjk. Matem. OB-Wa, Serija 2, T.13, 49–194 (1912) (Russisch).
Browder, F. E.: Functional analysis and partial differential equations. II. Math. Ann.145, 81–226 (1962).
Bruijn, N. G. de: Functions whose differences belong to a given class. Nieuw Archief voor Wiskunde (2)23, 194–218 (1951).
—— A difference property for Riemann integrable functions and for some similar classes of functions. Indagationes Math.14, 145–151 (1952).
Butzer, P. L., andW. Kozakiewicz: On the Riemann derivatives for integrable functions. Canad. J. Math.6, 572–581 (1954).
Calderon, A. P., andA. Zygmund: Local properties of solutions of elliptic partial differential equations. Studia Math.20, 171–225 (1961).
Carrol, F. W.: Functions whose differences belong toL p[0, 1]. Indagationes Math.26, 250–255 (1964).
Golovkin, K. K.: Some inequalities for the norms of mixed derivatives of functions of several variables. Soviet Math.5, 1628–1630 (1964); Doklady Akad. Nauk S.S.S.R.159.
Günzler, H.: Ein Identitätssatz für Lösungen quasilinearer hyperbolischer Differentialgleichungen. Math. Z.86, 337–360 (1964).
—— Beschränktheitseigenschaften von Lösungen nichtlinearer Wellengleichungen. Math. Ann.167, 75–104 (1966).
Hartman, Ph., andA. Wintner: On uniform Dini conditions in the theory of linear partial differential equations of elliptic type. Am. J. Math.77, 329–354 (1955).
Hellwig, G.: Partielle Differentialgleichungen. Stuttgart: Teubner 1960.
Hornich, H.: Zur Lösbarkeit der hyperbolischen Differentialgleichungen. Österr. Ing.-Arch.10, 195–197 (1956).
Jurkat, W. B.: On Cauchy's functional equation. Proc. Am. Math. Soc.16, 683–686 (1965).
Kestelman, H.: Modern Theories of Integration. New York: Dover Publ. 1960.
Mitjagin, B. S.: Über gewisse Eigenschaften von Funktionen zweier Veränderlicher. Vestnik Moskovsk. Univ., Ser. Mat. Mech. Astron. Fiz. Chim.14, No. 5, 137–152 (1960) (Russisch).
Schwartz, L.: Théorie des Distributions. I, II. Paris: Hermann 1957/1959.
Serrin, J.: On the differentiability of functions of several variables. Arch. Rat. Mech. Anal.7, 359–372 (1961).
Sobolev, S. L.: Sur les équations aux dérivées partielles hyperboliques non-linéaires. Monografie Matematiche Consiglio Naz. delle Richerche, 9. Rom: Edizioni Cremonese 1961.
Stein, E. M., andA. Zygmund: On the differentiability of functions. Studia Math.23, 247–283 (1964).
Wallen, L. J.: Advanced Problem No. 4879 (Bounded functions). Am. Math. Monthly68, 72 (1961).
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Herrn Prof. Dr.C. L. Siegel zum 70. Geburtstag gewidmet
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Günzler, H. Zur Regularität der Lösungen zweidimensionaler Wellengleichungen. Math. Ann. 169, 183–229 (1967). https://doi.org/10.1007/BF01399538
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DOI: https://doi.org/10.1007/BF01399538