5 problems

Strong-convergence conjecture. The renormalized sequence converges strongly:

Let $B_R\subset\mathbb{R}^N$ be the ball of radius $R$, let $2^*=\frac{2N}{N-2}$, and let $(u_k)_{k\geq 0}$ be radial solutions of the critical Lin–Ni–Takagi problem with exponent…

Global uniqueness conjecture. Solutions satisfying the physical jump condition are unique. Between jump times, the solution is continuously differentiable, and for every $t_0>0$ wi…

Let $N\geqslant 3$, let $i\geqslant 2$, and assume $2+oubles$?

Consider the semilinear parabolic problem denoted by equation … z=frac{x}{sqrt{(T-t)|log(T-t)|}}. … bar{fbeta}(z)=left(p-1+b(beta)|z|^2right)^{-frac{1}{p-1}}, … has a solution…