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MathGeo
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Eliminating 1st order terms in elliptic partial differential equation
@Hans can you recommend a reference for this "ground state transformation" you mentioned?
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Is there exists (strictly) convex function on hemisphere?
Sorry, is there any example of strictly convex function on $\mathbb{S}^n$?
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Existence of a special function
No. Note that I removed the second condition.
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Existence of a special function
Thank you. Could you give your opinion about the condition I removed, If we can get something close?
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Existence of a special function
Modify the question accordingly to get some ideas.
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Existence of a special function
You're right. I think I should at least modify the second condition. Now, I consider just the first one.
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Existence of a special function
@Lspice I don't see why it must be open and closed. I can assume it to be open w.r.t $\partial D$. The same value on whole domain is not what I need.
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A completion equality in product of Sobolev spaces
Thank you! Do you have any idea on how to change the set $\{ (f,f|_{\partial \Omega}), f\in C^{\infty}(\overline{\Omega}) \}$ to get an affirmative result?
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