The elliptic problems in a family of planar open sets. (English) Zbl 07144725

Tami, Abdelkader

Appl. Math., Praha 64, No. 5, 485-499 (2019).

This article is concerned with the study of singularities of solutions of the biharmonic equation \(\Delta^2 u=f(x)\) on a polygonal domain in the plane, subject to Dirichlet boundary conditions \(u=\Delta u=0\). The main concern here is the study of singularities which may appear near a corner points. The approach relies on Taylor expansion combined with uniform estimates with respect to the angle parameter.

Reviewer: Marius Ghergu (Dublin)

MSC:

35J25	Boundary value problems for second-order elliptic equations
35J40	Boundary value problems for higher-order elliptic equations
35J75	Singular elliptic equations
35B45	A priori estimates in context of PDEs
35Q99	Partial differential equations of mathematical physics and other areas of application
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

biharmonic operator; elliptic problems; nonsmooth boundaries; uniform singularity estimates; Sobolev spaces

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