Asymptotics of solutions near crack tips for Poisson equation with inequality type boundary conditions. (English) Zbl 1138.74043

Khludnev, A. M.; Kozlov, V. A.

Z. Angew. Math. Phys. 59, No. 2, 264-280 (2008).

Summary: We consider the Poisson equation in two-dimensional case for a nonsmooth domain. The geometrical domain has a cut (crack) where inequality-type boundary conditions are imposed. We analyze the behavior of solution near the crack tips. In particular, estimates for second derivatives in a weighted Sobolev space are obtained, and asymptotics of the solution near crack tips is established.

MSC:

74R10	Brittle fracture
74G10	Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
74G65	Energy minimization in equilibrium problems in solid mechanics
35Q72	Other PDE from mechanics (MSC2000)

Keywords:

Poisson equation; second derivatives; weighted Sobolev space