On weak minima of certain integral functionals
Gioconda Moscariello
Annales Polonici Mathematici, Tome 69 (1998), p. 37-48 / Harvested from The Polish Digital Mathematics Library

We prove a regularity result for weak minima of integral functionals of the form ΩF(x,Du)dx where F(x,ξ) is a Carathéodory function which grows as |ξ|p with some p > 1.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:270277
@article{bwmeta1.element.bwnjournal-article-apmv69z1p37bwm,
     author = {Gioconda Moscariello},
     title = {On weak minima of certain integral functionals},
     journal = {Annales Polonici Mathematici},
     volume = {69},
     year = {1998},
     pages = {37-48},
     zbl = {0920.49021},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv69z1p37bwm}
}
Gioconda Moscariello. On weak minima of certain integral functionals. Annales Polonici Mathematici, Tome 69 (1998) pp. 37-48. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv69z1p37bwm/

[000] [AF] E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal. 86 (1984), 125-145. | Zbl 0565.49010

[001] [Do] A. Dolcini, A uniqueness result for very weak solutions of p-harmonic type equations, Boll. Un. Mat. Ital. A (7) 10 (1996), 71-84. | Zbl 0854.35047

[002] [G] F. Gehring, Lp integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 265-277. | Zbl 0258.30021

[003] [GLS] D. Giachetti, F. Leonetti and R. Schianchi, On the regularity of very weak minima, Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), 287-296. | Zbl 0851.49026

[004] [Gi] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Ann. of Math. Stud. 105, Princeton Univ. Press, 1983.

[005] [GG] M. Giaquinta and E. Giusti, On the regularity of the minima of variational integrals, Acta Math. 148 (1982), 31-46. | Zbl 0494.49031

[006] [Gu] E. Giusti, Metodi diretti nel Calcolo delle Variazioni, Un. Mat. Ital., 1984.

[007] [GIS] L. Greco, T. Iwaniec and C. Sbordone, Variational integrals of nearly linear growth, preprint, Dip. di Mat. e Appl. R. Caccioppoli, Napoli. | Zbl 0889.35026

[008] [Iw] T. Iwaniec, p-Harmonic tensors and quasiregular mappings, Ann. of Math. 136 (1992), 589-624. | Zbl 0785.30009

[009] [IS] T. Iwaniec and C. Sbordone, Weak minima of variational integrals, J. Reine Angew. Math. 454 (1994), 143-161. | Zbl 0802.35016

[010] [Le] J. Lewis, On very weak solutions of certain elliptic systems, Comm. Partial Differential Equations 18 (1993), 1515-1537. | Zbl 0796.35061

[011] [Mo] G. Moscariello, Weak minima and quasiminima of variational integrals, Boll. Un. Mat. Ital. B 11 (1997), 355-364. | Zbl 0890.49003

[012] [Mu] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. | Zbl 0236.26016

[013] [Sb] C. Sbordone, Quasiminima of degenerate functionals with non polynomial growth, Rend. Sem. Mat. Fis. Milano 59 (1989), 173-184. | Zbl 0760.49023

[014] [To] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Pure and Appl. Math. 123, Academic Press, 1986.