Osservazioni sopra una classe di disuguaglianze
Tóm tắt
Si discute la disuguaglianza isoperimetrica:
$$\mathop \smallint \limits_0^l |u(x)|^p k(x)dx \leqslant costante,$$
dove k(x) è una funzione misurabile non negativa assegnata a u(x) è una funzione assolutamente continua verificante le condizioni:
$$u(0) = 0, \mathop \smallint \limits_0^l |u'(x)|^p dx = 1.$$
. We discuss the isoperimetric inequality:
$$\mathop \smallint \limits_0^l |u(x)|^p k(x)dx \leqslant costante,$$
where k(x) is a given nonnegative measurable function and u(x) is an absolutely continuous function subjected to the bounds:
$$u(0) = 0, \mathop \smallint \limits_0^l |u'(x)|^p dx = 1.$$
.
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