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manuscripta mathematica

, Volume 102, Issue 2, pp 227–250 | Cite as

Full C1,α-regularity for free and constrained local minimizers of elliptic variational integrals¶with nearly linear growth

  • Martin Fuchs
  • Giuseppe Mingione

Abstract:

We consider local minimizers \(\) of elliptic variational integrals \(\) with integrand f of nearly linear growth. In the scalar case N= 1 a side condition of the type u≥Φ may be incorporated, for N > 1 u is an unconstrained minimizer and f is required just to depend on the modulus of Du. We show in both cases that u has Hölder continuous first derivatives in the interior of the domain Ω.

Mathematics Subject Classification (1991):49N60, 35J50 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Martin Fuchs
    • 1
  • Giuseppe Mingione
    • 2
  1. 1.Universität des Saarlandes, Fachbereich 9 Mathematik, Postfach 15 11 50,¶66041 Saarbrücken, Germany. e-mail: fuchs@math.uni-sb.deDE
  2. 2.Dipartimento di Matematica, dell'Università di Parma, Via D'Azeglio 85/A, 43100 Parma, Italy. e-mail: mingione@prmat.math.unipr.itIT

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