Problèmes aux limites dans les polygones. Mode d’emploi. (Boundary value problems in plane polygons. Instructions for use). (French) Zbl 0623.35031

Grisvard, P.

Bull. Dir. Etud. Rech., Sér. C 1986, No. 1, 21-59 (1986).

This is a mere list of results describing the qualitative behaviour, near a corner, of the solutions of the most common elliptic boundary value problems in plane polygons. The operators under consideration are basically the Laplace operator, the biharmonic and the Lamé system (elasticity). The boundary conditions are of Dirichlet and Neumann type on complementary subsets of the boundary. These results are included in tables whenever possible.

MSC:

35J67	Boundary values of solutions to elliptic equations and elliptic systems
35J25	Boundary value problems for second-order elliptic equations
35J40	Boundary value problems for higher-order elliptic equations
35J55	Systems of elliptic equations, boundary value problems (MSC2000)

Keywords:

qualitative behaviour, near a corner; elliptic boundary value problems in plane polygons; Laplace operator; biharmonic; Lamé system; Dirichlet; Neumann