Recent content by agahlawa

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    Graduate Writing PDEs as differential equations on Hilbert space

    Sorry, was a typo. Fixed. Thank you.
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    Graduate Writing PDEs as differential equations on Hilbert space

    Hi, I was reading a paper on control of the 1-D heat equation with boundary control, the equation being \frac{\partial u(x,t)}{\partial x}= \frac{\partial^2 u(x,t)}{\partial x^2} with boundary conditions: u(0,t)=0 and u_x(1,t)=w(t), where w(t) is the control input. The authors...
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    Graduate Sobolev Spaces different definitions

    I got the answer. It's proven as an exercise. If the Sobolev space is defined for functions u: \mathbb{R} \rightarrow \mathbb{R} instead of u : \mathbb{R}^n \rightarrow \mathbb{R}, then the conditions can be reduced to the absolute continuity of the functions. Adi
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    Graduate Sobolev Spaces different definitions

    Hi, I am studying PDEs and I am confused by the definition of Sobolev spaces as they are different in two books. I'll write the definitions and mention the points of difference which I see despite which I still can't see the difference in definitions. 1) PDEs by Lawrence Evans Let U be...