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On the absence of Volterra correct restrictions and extensions of the Laplace operator
| Content Provider | Semantic Scholar |
|---|---|
| Author | Biyarov, Bazarkan Nuroldinovich |
| Copyright Year | 2016 |
| Abstract | At the beginning of the last century J. Hadamard constructed the well-known example illustrating the incorrectness of the Cauchy problem for elliptic-type equations. If the Cauchy problem for some differential equation is correct, then it is usually a Volterra problem, i.e., the inverse operator is a Volterra operator. At present, not a single Volterra correct restriction or extension for elliptic-type equations is known. In the present paper, we prove the absence of Volterra correct restrictions of the maximal operator $\widehat{L}$ and Volterra correct extensions of the minimal operator $L_0$ generated by the Laplace operator in $L_2(\Omega)$, where $\Omega$ is the unit disk. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1602.00092v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
