The energy integral of the calculus of variations, which we consider in this paper, has a limit behavior when the maximum exponent q, in the growth estimate of the integrand, reaches a threshold. In fact, if q is larger than this threshold, counterexamples to the local boundedness and regularity of minimizers are known. In this paper, we prove the local boundedness of minimizers (and also of quasi-minimizers) under this stated limit condition. Some other general and limit growth conditions are also considered.
Local Boundedness of Minimizers with Limit Growth Conditions / Cupini, Giovanni; Marcellini, Paolo; Mascolo, Elvira. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - STAMPA. - 166:(2015), pp. 1-22. [10.1007/s10957-015-0722-z]
Local Boundedness of Minimizers with Limit Growth Conditions
MARCELLINI, PAOLO;MASCOLO, ELVIRA
2015
Abstract
The energy integral of the calculus of variations, which we consider in this paper, has a limit behavior when the maximum exponent q, in the growth estimate of the integrand, reaches a threshold. In fact, if q is larger than this threshold, counterexamples to the local boundedness and regularity of minimizers are known. In this paper, we prove the local boundedness of minimizers (and also of quasi-minimizers) under this stated limit condition. Some other general and limit growth conditions are also considered.
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