ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35, 73 Kosmodem’yanskii, Alexander Arkadievitch, MIIT, Moscow, Russia On the location of fail points in Torsion Problem Let u(x, y) be the stress function of torsion problem.

Δu = −1, in D, u|_{Γ} = 0,

where D is the plane convex domain – cross section of the elastic bar and Γ is the boundary of D. The point M ∈ Γ is named the fail point, if |∇u(M)| = max_{Γ} |∇u|. We obtain the new results on the location of the fail points on Γ. For example, the point of the maximal curvaty of Γ is never be the fail point. The more precise results are obtained by comparison the solution u and the solution of the torsion problem in the rectangle. Reference: B. Kawohl, On the location of maxima of the gradient for solutions to qusilinear elliptic problems and a problem raised by Saint Venant, J. of Elasticity 17: (1987), 195 – 206.