Geodesic
Functional inequalities and generalized capacities
Sbornik. Mathematics, Tome 187 (1996) no. 1, pp. 39-52

Voir la notice de l'article provenant de la source Math-Net.Ru

In this criteria were found for the validity of a functional inequality of the form $\|f;Q\| \leqslant C\|\nabla f;P\|$, where $P$ and $Q$ are normed ideal spaces of functions on a domain $\Omega \subset \mathbb R^n$, and the constant $C$ is the same for compactly supported functions $f$ satisfying a Lipschitz condition. Conditions for norm agreement in the space $P$ and $Q$ are given under which the functional inequality in question is equivalent to a geometric inequality relating the $Q$-norms of the indicators and $P$-capacities of compact subset of $\Omega$. Estimates are given and general properties of the capacities are studied. 
@article{SM_1996_187_1_a2,
     author = {V. S. Klimov},
     title = {Functional inequalities and generalized capacities},
     journal = {Sbornik. Mathematics},
     pages = {39--52},
     publisher = {mathdoc},
     volume = {187},
     number = {1},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_1_a2/}
}
TY  - JOUR
AU  - V. S. Klimov
TI  - Functional inequalities and generalized capacities
JO  - Sbornik. Mathematics
PY  - 1996
SP  - 39
EP  - 52
VL  - 187
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1996_187_1_a2/
LA  - en
ID  - SM_1996_187_1_a2
ER  - 
%0 Journal Article
%A V. S. Klimov
%T Functional inequalities and generalized capacities
%J Sbornik. Mathematics
%D 1996
%P 39-52
%V 187
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1996_187_1_a2/
%G en
%F SM_1996_187_1_a2
V. S. Klimov. Functional inequalities and generalized capacities. Sbornik. Mathematics, Tome 187 (1996) no. 1, pp. 39-52. http://geodesic.mathdoc.fr/item/SM_1996_187_1_a2/