In our paper, we discuss the the problem of unique extension for abstract lower semicontinuous and translation invariant functionals from a class of regular functions to a class of less regular functions,by assuming a ”good” behaviour of functionals in relation to homotheties, suggested by a formula of homothetic change of variables. In particular, we apply these results to some integral functionals of the Calculus of Variation as the non-parametric area functional.
Homothetic changes of variables and the unique extension problem in Calculus of Variations
Perugia C.
2004-01-01
Abstract
In our paper, we discuss the the problem of unique extension for abstract lower semicontinuous and translation invariant functionals from a class of regular functions to a class of less regular functions,by assuming a ”good” behaviour of functionals in relation to homotheties, suggested by a formula of homothetic change of variables. In particular, we apply these results to some integral functionals of the Calculus of Variation as the non-parametric area functional.File in questo prodotto:
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