Outline to show equality in partial differential equations.

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Let $gamma in C^2(mathbbR^n)$. I would like to show the algebraic identity
$$gamma^-1/2( nabla cdot gamma nabla gamma^-1/2 ) = Delta - fracDelta gamma^1/2gamma^1/2.$$



I know this might seem trivial if the trick is seen but I seems to be stuck in some loophole. Could anyone gives a brief step through? Any hints will be much appreciated. Thanks!




multivariable-calculus pde operator-theory




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    up vote
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    down vote

    favorite












    Let $gamma in C^2(mathbbR^n)$. I would like to show the algebraic identity
    $$gamma^-1/2( nabla cdot gamma nabla gamma^-1/2 ) = Delta - fracDelta gamma^1/2gamma^1/2.$$



    I know this might seem trivial if the trick is seen but I seems to be stuck in some loophole. Could anyone gives a brief step through? Any hints will be much appreciated. Thanks!




    multivariable-calculus pde operator-theory




    share|cite|improve this question























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Let $gamma in C^2(mathbbR^n)$. I would like to show the algebraic identity
      $$gamma^-1/2( nabla cdot gamma nabla gamma^-1/2 ) = Delta - fracDelta gamma^1/2gamma^1/2.$$



      I know this might seem trivial if the trick is seen but I seems to be stuck in some loophole. Could anyone gives a brief step through? Any hints will be much appreciated. Thanks!




      multivariable-calculus pde operator-theory




      share|cite|improve this question













      Let $gamma in C^2(mathbbR^n)$. I would like to show the algebraic identity
      $$gamma^-1/2( nabla cdot gamma nabla gamma^-1/2 ) = Delta - fracDelta gamma^1/2gamma^1/2.$$



      I know this might seem trivial if the trick is seen but I seems to be stuck in some loophole. Could anyone gives a brief step through? Any hints will be much appreciated. Thanks!





      multivariable-calculus pde operator-theory





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








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