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Differentiability of minima of non-differentiable functionals. (English) Zbl 0513.49003


MSC:

49J10 Existence theories for free problems in two or more independent variables
26B05 Continuity and differentiation questions
26B35 Special properties of functions of several variables, Hölder conditions, etc.
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Citations:

Zbl 0494.49031
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References:

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[4] Giaquinta, M.: Multiple integrals in the Calculus of Variations and non linear elliptic systems, Vorlesungsreihe SFB 72 Bonn n.6 (1981) · Zbl 0498.49001
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[6] Giaquinta, M., Giusti, E.: On the regularity of the minima of variational integrals. Acta Math.148, 31-46 (1982) · Zbl 0494.49031
[7] Giaquinta, M., Giusti, E.: Quasi-minima, to appear · Zbl 0541.49008
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[9] Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin-Heidelberg-New York: Springer 1977 · Zbl 0361.35003
[10] Giusti, E.: Equazioni ellittiche del secondo ordine. Quaderni Unione Mat. Italiana n.6 (1978); Ed. Pitagora, Bologna · Zbl 1308.35001
[11] Giusti, E.: Regolarità parziale delle soluzioni di sistemi ellittici quasi lineari di ordine arbitrario. Ann. Scuola Norm. Sup. Pisa23, 115-141 (1969) · Zbl 0175.40102
[12] Giusti, E., Miranda, M.: Sulla regolarità delle soluzioni deboli di una classe di sistemi ellittici quasilineari. Arch. Rat. Mech. Anal.31, 173-184 (1968) · Zbl 0167.10703
[13] Ivert, P.A.: Partial regularity of vector valued functions minimizing variational integrals, preprint
[14] Ladyzhenskaya, O.A., Uraltseva, N.N.: Linear and quasilinear elliptic equations. New York: Acad. Press 1968 · Zbl 0164.13002
[15] Morrey, C.B., Jr.: Second order elliptic systems of differential equations. Ann. of Math. Studies n. 33, Princeton Univ. Press 1954, pp. 101-159 · Zbl 0057.08301
[16] Morrey, C.B., Jr.: Multiple integrals in the calculus of variations. Berlin-Heidelberg-New York: Springer 1966 · Zbl 0142.38701
[17] Morrey, C.B., Jr.: Partial regularity results for non linear elliptic systems. J. Math. and Mech.17, 649-670 (1968) · Zbl 0175.11901
[18] Phillips, D.: A minimization problem and the regularity of solutions in the presence of a free boundary, pre-print
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