Geodesic
On a family of extremum problems and the properties of an integral
Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 830-838

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

The following extremum problem is studied: $$ \int _0^1\bigl(y''(t)\bigr)^p\,dt\bigg/ \int _0^1\bigl(y'(t)\bigr)^q\,dt \to\min $$ over all $y$, with $y(0)=y(1)=0$ and $y'(0)=y'(1)=0$, which leads to the integral $$ \int_{\mathbb R}\bigl(\max(0,1+\mu x-|x|^q)\bigr)^{1/p'}\,dx $$ and yields exact estimates for the eigenvalues of differential operators in the generalized Lagrange problem on the stability of a column. 
@article{MZM_1998_64_6_a3,
     author = {A. P. Buslaev and V. A. Kondrat'ev and A. I. Nazarov},
     title = {On a family of extremum problems and the properties of an integral},
     journal = {Matemati\v{c}eskie zametki},
     pages = {830--838},
     publisher = {mathdoc},
     volume = {64},
     number = {6},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a3/}
}
TY  - JOUR
AU  - A. P. Buslaev
AU  - V. A. Kondrat'ev
AU  - A. I. Nazarov
TI  - On a family of extremum problems and the properties of an integral
JO  - Matematičeskie zametki
PY  - 1998
SP  - 830
EP  - 838
VL  - 64
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a3/
LA  - ru
ID  - MZM_1998_64_6_a3
ER  - 
%0 Journal Article
%A A. P. Buslaev
%A V. A. Kondrat'ev
%A A. I. Nazarov
%T On a family of extremum problems and the properties of an integral
%J Matematičeskie zametki
%D 1998
%P 830-838
%V 64
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a3/
%G ru
%F MZM_1998_64_6_a3
A. P. Buslaev; V. A. Kondrat'ev; A. I. Nazarov. On a family of extremum problems and the properties of an integral. Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 830-838. http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a3/