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

• Autorzy: Daniela Giachetti , Rosanna Schianchi
• 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.

Kategorie tematyczne

• 49N60: Regularity of solutions
• 35J60: Nonlinear elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 123
• Numer: 2
• Strony: 175-184

Daty

wydano

1997

otrzymano

1996-07-10

poprawiono

1996-09-23

Twórcy

autor

Daniela Giachetti

• 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

autor

Rosanna Schianchi

• 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

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.