The best constant in a mean-value trace inequality for functions of bounded variation on admissible domains in the Euclidean space is shown to agree with an isoperimetric constant associated with the domain. The existence and form of extremals is also discussed. Such result is exploited to compute the best constant in the relevant trace inequality when the domain is a ball. The existence and the form of extremals in this special case turn out to depend on the dimension of the Euclidean space.
A sharp trace inequality for functions of bounded variation in the ball / Andrea Cianchi. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - STAMPA. - 142:(2012), pp. 1179-1191. [10.1017/S0308210511000758]
A sharp trace inequality for functions of bounded variation in the ball
CIANCHI, ANDREA
2012
Abstract
The best constant in a mean-value trace inequality for functions of bounded variation on admissible domains in the Euclidean space is shown to agree with an isoperimetric constant associated with the domain. The existence and form of extremals is also discussed. Such result is exploited to compute the best constant in the relevant trace inequality when the domain is a ball. The existence and the form of extremals in this special case turn out to depend on the dimension of the Euclidean space.
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
