This article is cited in 4 scientific papers (total in 4 papers)
An analogue of St. Venant's principle for a polyharmonic equation and applications of it
I. N. Tavkhelidze
An a priori energy estimate analogous to the inequalities expressing St. Venant's principle in elasticity theory is obtained for the solution of a polyharmonic equation with the conditions of the first boundary-value problem in an $n$-dimensional domain. These estimates are used to study the behavior of the solution and its derivatives near irregular boundary points and at infinity as a consequence of the geometric properties of the boundary in a neighborhood of these points. Moreover, the estimates obtained are used to prove a uniqueness theorem for the solution of the Dirichlet problem in unbounded domains.
Bibliography: 13 titles.
PDF file (781 kB)
Mathematics of the USSR-Sbornik, 1983, 46:2, 237–253
MSC: Primary 31B30, 35B45, 35J40, 73C10; Secondary 35A05, 35J05, 35D99, 34A40, 46E35
I. N. Tavkhelidze, “An analogue of St. Venant's principle for a polyharmonic equation and applications of it”, Mat. Sb. (N.S.), 118(160):2(6) (1982), 236–251; Math. USSR-Sb., 46:2 (1983), 237–253
Citation in format AMSBIB
\paper An analogue of St.\,Venant's principle for a polyharmonic equation and applications of~it
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
V. A. Kondrat'ev, O. A. Oleinik, “Boundary-value problems for partial differential equations in non-smooth domains”, Russian Math. Surveys, 38:2 (1983), 1–66
A. E. Shishkov, “The Phragmén–Lindelöf principle for quasi-linear divergent higher order elliptic equations”, Russian Math. Surveys, 43:4 (1988), 237–238
S. P. Levashkin, “On the asymptotic properties of generalized solutions of Dirichlet's problem for a polyharmonic equation in non-smooth domains”, Russian Math. Surveys, 44:5 (1989), 208–209
G. V. Grishina, “Behavior of solutions of a nonlinear variational problem in a neighborhood of singular points of the boundary and at infinity”, Russian Acad. Sci. Sb. Math., 78:2 (1994), 333–355
|Number of views:|