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1997 | 123 | 2 | 175-184
Tytuł artykułu

Boundary higher integrability for the gradient of distributional solutions of nonlinear systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider distributional solutions to the Dirichlet problem for nonlinear elliptic systems of the type ${ div A(x, u, Du) = div f in Ω, u - u_0 ∈ W^{1,r}_0(Ω)$ with r less than the natural exponent p which appears in the coercivity and growth assumptions for the operator A. We prove that $Du ∈ W^{1,p}(Ω)$ if |r-p| is small enough.
Słowa kluczowe
Czasopismo
Rocznik
Tom
123
Numer
2
Strony
175-184
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-07-10
poprawiono
1996-09-23
Twórcy
  • Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Facoltà di Ingegneria, Università di Roma "La Sapienza", Via A. Scarpa 16, 00161 Roma, Italy, giachett@dmmm.uniroma1.it
  • Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Facoltà di Ingegneria, Università di Roma "La Sapienza", Via A. Scarpa 16, 00161 Roma, Italy, schianch@dmmm.uniroma1.it
Bibliografia
  • [1] H. Brezis, Analyse Fonctionnelle, théorie et applications, Masson, 1983.
  • [2] H. Federer, Geometric Measure Theory, Springer, Berlin, 1969.
  • [3] M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. of Math. Stud. 105, Princeton, 1983.
  • [4] M. Giaquinta and G. Modica, Regularity results for some classes of higher order nonlinear elliptic systems, J. Reine Angew. Math. 311//312 (1979), 145-169.
  • [5] E. Giusti, Metodi diretti del calcolo delle variazioni, Unione Matematica Italiana, 1994.
  • [6] T. Iwaniec, p-harmonic tensors and quasiregular mappings, Ann. of Math. 136 (1992), 589-624.
  • [7] T. Iwaniec and C. Sbordone, Weak minima of variational integrals, J. Reine Angew. Math. 454 (1994), 143-161.
  • [8] T. Iwaniec, C. Scott and B. Stroffolini, Nonlinear Hodge theory on manifolds with boundary, preprint.
  • [9] D. Giachetti, F. Leonetti and R. Schianchi, On the regularity of very weak minima, Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), 287-296.
  • [10] D. Giachetti, F. Leonetti and R. Schianchi, Boundary regularity and uniqueness for very weak A harmonic functions, in preparation.
  • [11] N. Meyers, An $L^p$-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa 17 (1963), 189-206.
  • [12] N. Meyers and A. Elcrat, Some results on regularity for solutions of non-linear elliptic systems and quasi-regular functions, Duke Math. J. 42 (1975), 121-136.
  • [13] G. Moscariello, Weak minima and quasiminima of variational integrals, Boll. Un. Mat. Ital., to appear.
  • [14] G. Moscariello, On weak minima of certain integral functionals, preprint.
  • [15] B. Stroffolini, On weakly A-harmonic tensors, Studia Math. 114 (1995), 289-301.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv123i2p175bwm
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