On the differentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator (Q554843)
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scientific article; zbMATH DE number 5930227
| Language | Label | Description | Also known as |
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| English | On the differentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator |
scientific article; zbMATH DE number 5930227 |
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On the differentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator (English)
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22 July 2011
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Summary: For the evolution equation \(y'(t) = Ay(t)\), with a scalar type spectral operator \(A\) in a Banach space, conditions on \(A\) are found that are necessary and sufficient for all weak solutions of the equation on \([0, \infty)\) to be strongly infinitely often differentiable. Certain effects of smoothness improvement of the weak solutions are analyzed.
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