Existence of discontinuous absolute minima for certain multiple integrals without growth properties

Cesari, Lamberto. "Existence of discontinuous absolute minima for certain multiple integrals without growth properties." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.4 (1988): 661-671. <http://eudml.org/doc/287250>.

@article{Cesari1988,
abstract = {In the present paper the author discusses certain multiple integrals $I(u)$ of the calculus of variations satisfying convexity conditions, and no growth property, and the corresponding Serrin integrals $\mathfrak\{I\}(u)$, to which the existence theorems in [3,4,5] do not apply. However, in the present paper, the integrals $I(u)$ and $\mathfrak\{I\}(u)$ are reduced to simpler form $H(v)$ and $\mathcal\{H\}(v)$ to which the existence theorems above apply. Thus, we derive that $I(u) \le \mathfrak\{I\}(u)$, $H(v) \le \mathcal\{H\}(v)$, we obtain the existence of the absolute minimum for the Serrin forms $\mathfrak\{I\}(u)$ and $\mathcal\{H\}(v)$, and such minimum is given by BV functions, possibly discontinuous and not of Sobolev.},
author = {Cesari, Lamberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {BV function; Property (Q); Property (F); Serrin integral; multiple integrals; Serrin integrals},
language = {eng},
month = {12},
number = {4},
pages = {661-671},
publisher = {Accademia Nazionale dei Lincei},
title = {Existence of discontinuous absolute minima for certain multiple integrals without growth properties},
url = {http://eudml.org/doc/287250},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Cesari, Lamberto
TI - Existence of discontinuous absolute minima for certain multiple integrals without growth properties
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/12//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 4
SP - 661
EP - 671
AB - In the present paper the author discusses certain multiple integrals $I(u)$ of the calculus of variations satisfying convexity conditions, and no growth property, and the corresponding Serrin integrals $\mathfrak{I}(u)$, to which the existence theorems in [3,4,5] do not apply. However, in the present paper, the integrals $I(u)$ and $\mathfrak{I}(u)$ are reduced to simpler form $H(v)$ and $\mathcal{H}(v)$ to which the existence theorems above apply. Thus, we derive that $I(u) \le \mathfrak{I}(u)$, $H(v) \le \mathcal{H}(v)$, we obtain the existence of the absolute minimum for the Serrin forms $\mathfrak{I}(u)$ and $\mathcal{H}(v)$, and such minimum is given by BV functions, possibly discontinuous and not of Sobolev.
LA - eng
KW - BV function; Property (Q); Property (F); Serrin integral; multiple integrals; Serrin integrals
UR - http://eudml.org/doc/287250
ER -