# coercivity vs boundedness of operator

hi,

the definition of coercivity and boundedness of a linear operator L between two B spaces looks similar: $\|Lx\|\ge M _ 1\|x\|$ and $||Lx||\le M _ 2\|x\|$ for some constants $M _ 1$ and $M _ 2$. Thus in order to show the existence of a PDE $Lu=f$ one needs to show that it is coercive. However if my operator $L$ happen to be bounded and $M _ 2 < M _ 1$ can I prove existence?

What is the intuition behind those two concepts because they are based on computation of the same quantities and comparing the two?

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–  Will Jagy Mar 23 '12 at 21:01
–  Will Jagy Mar 23 '12 at 22:23