| 1. | Sobolev spaces are often considered when investigating partial differential equations.
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| 2. | There exist other generalizations of the Poincar?inequality to other Sobolev spaces.
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| 3. | Moreover, they leave invariant each of the Sobolev spaces.
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| 4. | They carry each Sobolev space into the Schwartz functions.
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| 5. | In this case the original operator defines a Fredholm operator between the Sobolev spaces.
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| 6. | Let be the complement of } } and define restricted Sobolev spaces analogously for.
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| 7. | Enlargements of the Sobolev spaces ( ? ) } } have to be considered.
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| 8. | The Sobolev space is defined to the Hilbert space completion of this space for the norm
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| 9. | Their action on L " p " and Sobolev spaces is discussed in.
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| 10. | A precise definition and proof of the decomposition requires the problem to be formulated on Sobolev spaces.
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