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Math Help - express it as an eigenvalue problem (sobolev)

  1. #1
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    express it as an eigenvalue problem (sobolev)

    Hello

    The exercise is given by

    Express

     sup_{v \in V \setminus \{0\}} \frac{\int_0^1 v*v}{\int_0^1 v'*v'} as an eigenvalue problem where  V \subset W^{1,2}(\]0.1\[) and \forall v \in V : v(0)=0=v(1)

    ( W^{k,p}(\]0,1\[) denotes the sobolev space on the open intervall (0,1). For those who don't know that just assume V is a subspace of functions on this intervall with boundary values of 0 that have the first order derivative.)

    I don't know how to begin this. I have to find something in the way A*x=b where A is a given matrix, b is a given vector and x the solution that has to be found. But how can I do this? Or even better I just have to find a matrix which (absolute) greatest eigenvalue determines this value?

    I tried partial integration but it really leads me nowhere... Does anyone have a hint how to solve this?

    Regards
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  2. #2
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    Re: express it as an eigenvalue problem (sobolev)

    Does noone have a hint or such? How can this be transformed into an eigenvalue problem?
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