Self-adjointness of elliptic operator with growing coefficients (Q2704767)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Self-adjointness of elliptic operator with growing coefficients |
scientific article |
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12 March 2001
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elliptic operator
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self-adjoint operator
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strong solution
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weighted Hilbert space
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Self-adjointness of elliptic operator with growing coefficients (English)
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The author considers a second order elliptic operator \( A_{a} \) with coefficients growing at infinity as \(|x|^a\), \( a \leq 2\). It is shown that \( 1-A_{a} \) is symmetric and strictly monotone on \( C_{0}^{\infty} (\mathbb{R}^n)\), respectively on an appropriate weighted Hilbert space. The main result of this paper claims that the operator \( 1-A_{a} \) has a self adjoint closure. Moreover, it is proved that each weak solution of the equation \( (1-A_{a})u = f \) is also a strong one.
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