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On the Dirichlet Problem with Corner Singularity
| Content Provider | MDPI |
|---|---|
| Author | Rukavishnikov, Viktor Rukavishnikova, Elena |
| Copyright Year | 2020 |
| Description | 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. |
| Starting Page | 1870 |
| e-ISSN | 22277390 |
| DOI | 10.3390/math8111870 |
| Journal | Mathematics |
| Issue Number | 11 |
| Volume Number | 8 |
| Language | English |
| Publisher | MDPI |
| Publisher Date | 2020-10-29 |
| Access Restriction | Open |
| Subject Keyword | Mathematics Mathematical Physics Corner Singularity Boundary-value Problem Rν-generalized Solution Existence and Uniqueness Solution |
| Content Type | Text |
| Resource Type | Article |
