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2009, Volume 11, Issue 1: 31-42. Doi: 10.3934/dcdsb.2009.11.31
This issue Previous Article Fastness and continuous dependence in front propagation in Fisher-KPP equations Next Article Higher integrability for minimizers of anisotropic functionals

A nonlinear interpolation result with application to the summability of minima of some integral functionals

  • 1.

    Dipartimento di Matematica, Università di Roma 1, Piazza A. Moro 2, 00185 Roma

  • 2.

    Dip. Metodi e Modelli Matematici per le Scienze Applicate, Univ. Roma 1, Via Antonio Scarpa 16, 00161 Roma

Received:  December 31, 2007
Revised:  March 31, 2008
Published:  June 2009
Abstract Related Papers Cited by
    Abstract
  • We shall prove results asserting the (global) $L^s$-summability of the minima of integral functionals, using the classical structural assumptions. A feature of the method is that it depends not so much on the minimization problem but rather on the "control from below'' of the structural assumptions. Then the proof concerning the summability of the minima of integral functionals can be easily adapted in order to prove the summability of solutions of nonlinear elliptic equations (even when they are not Euler equations of functionals).
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:
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