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Generalized gradients and applications. (English) Zbl 0307.26012


MSC:

26B35 Special properties of functions of several variables, Hölder conditions, etc.
26A51 Convexity of real functions in one variable, generalizations
26B05 Continuity and differentiation questions
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References:

[1] Jean-Michel Bony, Principe du maximum, inégalite de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés, Ann. Inst. Fourier (Grenoble) 19 (1969), no. fasc. 1, 277 – 304 xii (French, with English summary). · Zbl 0176.09703
[2] Haïm Brezis, On a characterization of flow-invariant sets, Comm. Pure Appl. Math. 23 (1970), 261 – 263. · Zbl 0191.38703 · doi:10.1002/cpa.3160230211
[3] F. H. Clarke, Necessary conditions for nonsmooth problems in optimal control and the calculus of variations, Thesis, University of Washington, 1973.
[4] -, Necessary conditions for nonsmooth variational problems (Proc. Fourteenth Biennial Sem. Canad. Math. Congr., 1974), Springer-Verlag, New York (to appear). · Zbl 0327.49015
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[8] William Hogan, Directional derivatives for extremal-value functions with applications to the completely convex case, Operations Res. 21 (1973), 188 – 209. Mathematical programming and its applications. · Zbl 0278.90062
[9] B. N. Pshenichnyi, Necessary conditions for an extremum, Translated from the Russian by Karol Makowski. Translation edited by Lucien W. Neustadt. Pure and Applied Mathematics, vol. 4, Marcel Dekker, Inc., New York, 1971. · Zbl 0764.90079
[10] R. M. Redheffer, The theorems of Bony and Brezis on flow-invariant sets, Amer. Math. Monthly 79 (1972), 740 – 747. · Zbl 0278.34039 · doi:10.2307/2316263
[11] R. Tyrrell Rockafellar, Convex analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, N.J., 1970. · Zbl 0193.18401
[12] R. T. Rockafellar, Conjugate convex functions in optimal control and the calculus of variations, J. Math. Anal. Appl. 32 (1970), 174 – 222. · Zbl 0218.49004 · doi:10.1016/0022-247X(70)90324-0
[13] R. T. Rockafellar, Existence and duality theorems for convex problems of Bolza, Trans. Amer. Math. Soc. 159 (1971), 1 – 40. · Zbl 0255.49007
[14] Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. · Zbl 0207.13501
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