A priori estimates for nonlinear elliptic complexes

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

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

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 Lp logα L(ω). It is the first time the regularity results for genuine nonisotropic PDEs have been successfully treated. Recent advances in harmonic analysis, especially the H1-BMO duality theory, play the key role in our arguments. Applications to the geometric function theory are already in place [16].

Original languageEnglish (US)
Pages (from-to)513-546
Number of pages34
JournalAdvances in Differential Equations
Volume8
Issue number5
StatePublished - Dec 1 2003

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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    Iwaniec, T., Migliaccio, L., Moscariello, G., & di Napoli, A. P. (2003). A priori estimates for nonlinear elliptic complexes. Advances in Differential Equations, 8(5), 513-546.