Estimation of the best constant involving the L² norm of the higher‐order Wente problem

Abstract

We study the best constant involving theL2norm of thep-derivative solution of Wente's problem inℝ2p. We prove that this best constant is achieved by the choice of some functionu. We give also explicitly the expression of this constant in the special casep=2.

The Wente problem associated to the modified Helmholtz operator

“…By the same arguments, replacing Ω by R 2 , and using that C 0 2 (R 2 ) = √ 3/32π (see [5,12]), we obtain that…”