DeepAI AI Chat
Log In Sign Up

Regularity of the solution of the scalar Signorini problem in polygonal domains

by   Thomas Apel, et al.
Universität der Bundeswehr München
Université Polytechnique Hauts-de-France

The Signorini problem for the Laplace operator is considered in a general polygonal domain. It is proved that the coincidence set consists of a finite number of boundary parts plus isolated points. The regularity of the solution is described. In particular, we show that the leading singularity is in general r_i^π/(2α_i) at transition points of Signorini to Dirichlet or Neumann conditions but r_i^π/α_i at kinks of the Signorini boundary, with α_i being the internal angle of the domain at these critical points.


page 1

page 2

page 3

page 4


A Steklov-spectral approach for solutions of Dirichlet and Robin boundary value problems

In this paper we revisit an approach pioneered by Auchmuty to approximat...

On the discretization of Laplace's equation with Neumann boundary conditions on polygonal domains

In the present paper we describe a class of algorithms for the solution ...

Wavenumber-explicit hp-FEM analysis for Maxwell's equations with impedance boundary conditions

The time-harmonic Maxwell equations at high wavenumber k in domains with...

On a Boundary Updating Method for the Scalar Stefan Problem

We report on a general purpose method for the scalar Stefan problem insp...

Power-SLIC: Diagram-based superpixel generation

Superpixel algorithms, which group pixels similar in color and other low...

On the Smoothness of the Solution to the Two-Dimensional Radiation Transfer Equation

In this paper, we deal with the differential properties of the scalar fl...

Weak discrete maximum principle of isoparametric finite element methods in curvilinear polyhedra

The weak maximum principle of the isoparametric finite element method is...