We study the regularity of finite energy solutions to degenerate n-harmonic equations. The function K(x), which measures the degeneracy, is assumed to be subexponentially integrable, i.e. it verifies the condition exp(P(K)) ∈ Lloc1. The function P(t) is increasing on [0,∞[ and satisfies the divergence condition
Mots-clés : Orlicz classes, degenerate elliptic equations, continuity
@article{COCV_2012__18_3_621_0,
author = {Giannetti, Flavia and Passarelli di Napoli, Antonia},
title = {On the continuity of degenerate $n$-harmonic functions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {621--642},
publisher = {EDP-Sciences},
volume = {18},
number = {3},
year = {2012},
doi = {10.1051/cocv/2011164},
zbl = {1258.35044},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2011164/}
}
TY - JOUR AU - Giannetti, Flavia AU - Passarelli di Napoli, Antonia TI - On the continuity of degenerate $n$-harmonic functions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 621 EP - 642 VL - 18 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2011164/ DO - 10.1051/cocv/2011164 LA - en ID - COCV_2012__18_3_621_0 ER -
%0 Journal Article %A Giannetti, Flavia %A Passarelli di Napoli, Antonia %T On the continuity of degenerate $n$-harmonic functions %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 621-642 %V 18 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2011164/ %R 10.1051/cocv/2011164 %G en %F COCV_2012__18_3_621_0
Giannetti, Flavia; Passarelli di Napoli, Antonia. On the continuity of degenerate $n$-harmonic functions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 621-642. doi : 10.1051/cocv/2011164. http://archive.numdam.org/articles/10.1051/cocv/2011164/
[1] and , An approximation lemma for W1,p functions, in Material Instabilities in Continuum Mechanics, J.M. Ball Ed. (Edinburgh, 1985-1986). Oxford University Press, New York (1988). | MR | Zbl
[2] , and , Regularity for p-harmonic equations with right hand side in Orlicz-Zygmund classes. J. Differ. Equ. 242 (2007) 248-268. | MR | Zbl
[3] , Rings and quasiconformal mapping in the space. Trans. Amer. Math. Soc. 103 (1962) 353-393. | MR | Zbl
[4] and , Isoperimetric type inequalities for differential forms on manifolds. Indiana Univ. Math. J. 54 (2005) 1483-1497. | MR | Zbl
[5] and , On very weak solutions of degenerate equations. NoDEA 14 (2007) 739-751. | MR | Zbl
[6] , and , The self-improving property of the Jacobian determinant in Orlicz spaces. Indiana Univ. Math. J. 59 (2010) 91-114. | MR | Zbl
[7] , and , Regularity of solutions of degenerate A-harmonic equations. Nonlinear Anal. 73 (2010) 2651-2665. | MR | Zbl
[8] and , Continuity estimates for n-harmonic equations. Indiana Univ. Math. J. 56 (2007) 805-824. | MR | Zbl
[9] and , Quasiharmonic fields. Ann. Inst. Henri Poincaré Anal. non Linéaire 18 (2001) 519-572. | Numdam | MR | Zbl
[10] , , and , A priori estimates for nonlinear elliptic complexes. Advances Difference Equ. 8 (2003) 513-546. | MR | Zbl
[11] , , , and , Mappings of finite distortion : sharp Orlicz conditions. Rev. Mat. Iberoamericana 19 (2003) 857-872. | EuDML | MR | Zbl
[12] and , Mappings of finite distortion : the sharp modulus of continuity. Trans. Amer. Math. Soc. 355 (2003) 1905-1920. | MR | Zbl
[13] , and , Regularity theory and traces of 𝒜-harmonic functions. Trans. Amer. Math. Soc. 348 (1996) 755-766. | MR | Zbl
[14] and , Convex Functions and Orlicz Spaces. P. Noordhoff LTD, Groningen, The Netherlands (1961). | Zbl
[15] , On very weak solutions of certain elliptic systems. Commun. Partial. Differ. Equ. 18 (1993) 1515-1537. | MR | Zbl
[16] , Weakly monotone functions. J. Geom. Anal. 4 (1994) 393-402. | MR | Zbl
[17] , On the integrability of “finite energy” solutions for p-harmonic equations. NoDEA 11 (2004) 393-406. | MR | Zbl
[18] and , Theory of Orlicz spaces. Monographs and Textbooks in Pure and Applied Mathematics 146. Marcel Dekker, Inc., New York (1991). | MR | Zbl
[19] , Équations elliptiques du second ordre à coefficients discontinus. Semin. de Math. Supérieures 16, Univ. de Montréal (1966). | MR | Zbl
Cité par Sources :
