On the solvability of the equation \( \text{div} \, u=f\) in \(L^1\) and in \(C^0\) (Q2368624)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the solvability of the equation \( \text{div} \, u=f\) in \(L^1\) and in \(C^0\) |
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On the solvability of the equation \( \text{div} \, u=f\) in \(L^1\) and in \(C^0\) (English)
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26 April 2006
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Summary: We show that the equation \(\text{div} \, u =f\) has, in general, no Lipschitz (respectively \(W^{1, 1}\)) solution if \(f\) is \(C^0\) (respectively \(L^1\)).
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divergence
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Lorentz spaces
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Sobolev imbedding theorem
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