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Manuscripta Mathematica

, Volume 137, Issue 3–4, pp 287–315 | Cite as

Local boundedness of solutions to quasilinear elliptic systems

  • Giovanni Cupini
  • Paolo MarcelliniEmail author
  • Elvira Mascolo
Article

Abstract

The mathematical analysis to achieve everywhere regularity in the interior of weak solutions to nonlinear elliptic systems usually starts from their local boundedness. Having in mind De Giorgi’s counterexamples, some structure conditions must be imposed to treat systems of partial differential equations. On the contrary, in the scalar case of a general elliptic single equation a well established theory of regularity exists. In this paper we propose a unified approach to local boundedness of weak solutions to a class of quasilinear elliptic systems, with a structure condition inspired by Ladyzhenskaya–Ural’tseva’s work for linear systems, as well as valid for the general scalar case. Our growth assumptions on the nonlinear quantities involved are new and general enough to include anisotropic systems with sharp exponents and the p, q-growth case.

Mathematics Subject Classification (2000)

Primary: 35J47 Secondary: 35J62 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Giovanni Cupini
    • 1
  • Paolo Marcellini
    • 2
    Email author
  • Elvira Mascolo
    • 2
  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly
  2. 2.Dipartimento di Matematica “U. Dini”Università di FirenzeFirenzeItaly

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