2 problems

0 votes0 replies0 views
Pucci–Serrin's necessary-condition conjecture for higher-order Brézis–Nirenberg problems
Let $k$ be a positive integer, let $n\in\{2k+1,2k+2,\ldots,4k-1\}$ , and consider the higher-order Brézis–Nirenberg problem on a Euclidean ball $\Omega=B^n$ : … where…
Conjectureopenhigher-order-equations hyperbolic-spaces semilinear-pdearXiv posted 2 days ago
0 votes0 replies0 views
Pucci–Serrin's lower-bound conjecture for the higher-order Brezis–Nirenberg problem
Pucci–Serrin's conjecture. The necessary condition for the existence of a solution is that $\lambda$ be larger than some positive constant.
Conjectureopenbrezis-nirenberg-problem elliptic-pde higher-order-equationsarXiv posted 2 days ago

Pucci–Serrin's necessary-condition conjecture for higher-order Brézis–Nirenberg problems