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

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January 2009, 11(1): 31-42. doi: 10.3934/dcdsb.2009.11.31

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

Lucio Boccardo ^1, and Daniela Giachetti ^2,

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, Italy

Received January 2008 Revised April 2008 Published November 2008

Abstract
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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).

Keywords: multifractal analysis, Dimension theory, Poincaré recurrences.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation: Lucio Boccardo, Daniela Giachetti. A nonlinear interpolation result with application to the summability of minima of some integral functionals. Discrete & Continuous Dynamical Systems - B, 2009, 11 (1) : 31-42. doi: 10.3934/dcdsb.2009.11.31

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