On the Dirichlet Problem with Corner Singularity

Viktor A. Rukavishnikov and Elena I. Rukavishnikova
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Viktor A. Rukavishnikov: Computing Center of Far-Eastern Branch, Russian Academy of Sciences, Kim-Yu-Chen Str. 65, 680000 Khabarovsk, Russia
Elena I. Rukavishnikova: Computing Center of Far-Eastern Branch, Russian Academy of Sciences, Kim-Yu-Chen Str. 65, 680000 Khabarovsk, Russia

Mathematics, 2020, vol. 8, issue 11, 1-7

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 R ν -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 R ν -generalized solution in set W ? 2 , α 1 ( Ω , δ ) is proven. The R ν -generalized solution is the same for different parameters ν .

Keywords: corner singularity; boundary-value problem; R ? -generalized solution; existence and uniqueness solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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