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ArticleOriginal scientific text

Title

On weak minima of certain integral functionals

Authors 1

Affiliations

  1. D.I.I.M.A., Università Degli Studi di Salerno, Via S. Allende, 84081 Baronissi (SA), Italy

Abstract

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.

Keywords

ENG
weak minimizer, maximal functions

Bibliography

  1. [AF] E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal. 86 (1984), 125-145.
  2. [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.
  3. [G] F. Gehring, Lp integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 265-277.
  4. [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.
  5. [Gi] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Ann. of Math. Stud. 105, Princeton Univ. Press, 1983.
  6. [GG] M. Giaquinta and E. Giusti, On the regularity of the minima of variational integrals, Acta Math. 148 (1982), 31-46.
  7. [Gu] E. Giusti, Metodi diretti nel Calcolo delle Variazioni, Un. Mat. Ital., 1984.
  8. [GIS] L. Greco, T. Iwaniec and C. Sbordone, Variational integrals of nearly linear growth, preprint, Dip. di Mat. e Appl. R. Caccioppoli, Napoli.
  9. [Iw] T. Iwaniec, p-Harmonic tensors and quasiregular mappings, Ann. of Math. 136 (1992), 589-624.
  10. [IS] T. Iwaniec and C. Sbordone, Weak minima of variational integrals, J. Reine Angew. Math. 454 (1994), 143-161.
  11. [Le] J. Lewis, On very weak solutions of certain elliptic systems, Comm. Partial Differential Equations 18 (1993), 1515-1537.
  12. [Mo] G. Moscariello, Weak minima and quasiminima of variational integrals, Boll. Un. Mat. Ital. B 11 (1997), 355-364.
  13. [Mu] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.
  14. [Sb] C. Sbordone, Quasiminima of degenerate functionals with non polynomial growth, Rend. Sem. Mat. Fis. Milano 59 (1989), 173-184.
  15. [To] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Pure and Appl. Math. 123, Academic Press, 1986.
Annales Polonici Mathematici
1998/69/1
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Pages:
37-48
Main language of publication
English
Received
1997-01-23
Published
1998
Exact and natural sciences