Local boundedness of minimizers in a limit case. (English) Zbl 0722.49012

Fusco, Nicola; Sbordone, Carlo

Manuscr. Math. 69, No. 1, 19-25 (1990).

Summary: We prove the local boundedness of minimizers of a functional with anisotropic polynomial growth. The result here obtained is optimal if compared with previously known counterexamples [see M. Giaquinta, Manuscr. Math. 59, 245-248 (1987; Zbl 0638.49005); P. Marcellini, J. Differ. Equations 90, No.1, 1-30 (1991); “Un example de solution discontinue d’un problème variationnel dans le cas scalaire”, preprint, Firenze: Univ. degli Studii, Ist. Mat. “Ulisse Dini”, No.11 (1987); M. Hong, “Some remarks on the minimizers of variational integrals with non-standard growth conditions”, preprint].

MSC:

49J40	Variational inequalities
49J45	Methods involving semicontinuity and convergence; relaxation

Keywords:

local boundedness; anisotropic polynomial growth

Citations:

Zbl 0638.49005

References:

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