Sobolev space
We define the Sobolev spaces of functions where is an open subset of , is an integer and .
The spaces are simply defined to be the spaces of Lebesgue -summable functions. We then define the space to be the space of functions which have weak derivatives such that .
The space turns out to be a Banach space when endowed with the norm
i.e.Β the sum of the norms of and of all weak derivatives of up to the -th order.
Of particular interest are the spaces which turn out to be Hilbert spaces with the scalar product given by
Title | Sobolev space |
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Canonical name | SobolevSpace |
Date of creation | 2013-03-22 14:54:55 |
Last modified on | 2013-03-22 14:54:55 |
Owner | paolini (1187) |
Last modified by | paolini (1187) |
Numerical id | 10 |
Author | paolini (1187) |
Entry type | Definition |
Classification | msc 46E35 |
Synonym | Sobolev function |
Related topic | WeakDerivative |