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Jul 7, 2015 at 18:56

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So when i write $Lu=f$ with $ f \in L^2$ what does it mean? It means that they are the same operator, so they are the same element of $H^{-1}$?

Jul 7, 2015 at 18:53

revised

Operator on a Sobolev space

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Jul 7, 2015 at 18:51

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Operator on a Sobolev space

Thanks. So, every operator $L$ in this form, BY DEFINITION, act in a particular way that doesn't count second derivaties?

Jul 7, 2015 at 18:35

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Operator on a Sobolev space

Thanks. Isn't this the bilinear form $B[u,v]$ associated with $L$? So what's the difference between $L$ and $B[u,v]$? $$ \langle Lu,v\rangle = \int_\Omega -a_{ij}D_juD_iv+b_iD_iuv+cuv. $$

Jul 7, 2015 at 16:40

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Operator on a Sobolev space

Jul 7, 2015 at 16:24

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