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Feb
1
awarded  Scholar
Feb
1
comment A 'conjecture' on critical elliptic pde
Craig, thanks for telling me this technique. I also realized that the answer should be straight forward from the known result. Assume $u$ is a solution to the problem (with certain regularity, for example, $C^1$), then extend $u$ by zero to the whole space, then we must have $u=0$ by the characterization of solutions to the cauchy problem $\Delta u+u^5=0$ in $\mathbb{R}^3$.
Feb
1
accepted A 'conjecture' on critical elliptic pde
Jan
5
comment A 'conjecture' on critical elliptic pde
Yes, I want zero boundary condition.
Jan
5
asked A 'conjecture' on critical elliptic pde
Jan
4
asked A critical elliptic PDE
Dec
29
awarded  Student
Dec
29
asked Best constant of Gagliardo-Nirenberg inequality in exterier domain