Advances in Differential Equations

A priori estimates for nonlinear elliptic complexes

Tadeusz Iwaniec, Lucia Migliaccio, Gioconda Moscariello, and Antonia Passarelli di Napoli

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We give a priori estimates for nonlinear partial differential equations in which the ellipticity bounds degenerate. The so-called distortion function which measures the degree of degeneracy of ellipticity is exponentially integrable, thus not necessarily bounded. The right spaces of the gradient of the solutions to such equations turn out to be the Orlicz-Zygmund spaces $L^p\log^\alpha L(\Omega)$. It is the first time the regularity results for genuine nonisotropic PDEs have been successfully treated. Recent advances in harmonic analysis, especially the ${\mathcal H }^{1}-BMO$ duality theory, play the key role in our arguments. Applications to the geometric function theory are already in place [16].

Article information

Adv. Differential Equations, Volume 8, Number 5 (2003), 513-546.

First available in Project Euclid: 19 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J45
Secondary: 30C65: Quasiconformal mappings in $R^n$ , other generalizations 35B45: A priori estimates 35J60: Nonlinear elliptic equations 35J70: Degenerate elliptic equations


Iwaniec, Tadeusz; Migliaccio, Lucia; Moscariello, Gioconda; Passarelli di Napoli, Antonia. A priori estimates for nonlinear elliptic complexes. Adv. Differential Equations 8 (2003), no. 5, 513--546.

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