On the Dirichlet Problem with Corner Singularity
Viktor A. Rukavishnikov, Elena I. Rukavishnikova
Abstract
We consider the Dirichlet problem for an elliptic equation with a singularity. The singularity of the solution to the problem is caused by the presence of a re-entrant corner at the boundary of the domain. We define an Rν-generalized solution for this problem. This allows for the construction of numerical methods for finding an approximate solution without loss of accuracy. In this paper, the existence and uniqueness of the Rν-generalized solution in set W∘2,α1(Ω,δ) is proven. The Rν-generalized solution is the same for different parameters ν.
Topics & Concepts
SingularityUniquenessMathematicsDirichlet problemDomain (mathematical analysis)Mathematical analysisDirichlet boundary conditionElliptic curveBoundary (topology)Boundary value problemApplied mathematicsDifferential Equations and Boundary ProblemsDifferential Equations and Numerical MethodsAdvanced Mathematical Modeling in Engineering