Work

Existence results for elliptic equation involving polyharmonic operator and a critical growth

Year: 2024

Type: article

Abstract: In this work, we study the two following minimization problems for $$r \in \mathbb {N}^{*}$$ r ∈ N ∗ , $$\begin{aligned} \begin{array}{ccc} S_{0,r}(\varphi )=\displaystyle \inf _{u\in H_{0}^{r}(\Omega ),\,\Vert u+\varphi \Vert _{L^{2^{*r}}}=1}\Vert u\Vert _{r}^{2}&\text { and }\,\,&S_{\theta ,r}(\varphi )=\displaystyle \inf _{u\in H_{\theta }^{r}(\Omega ),\,\Vert u+\varphi \Vert _{L^{2^{*r}}}=1}\Vert u\Vert _{r}^{2}, \end{array} \end{aligned}$$ S 0 , r ( φ ) = inf u ∈ H 0 r ( Ω ) , ‖ u + φ ‖ L 2 ∗ r = 1 ‖ u ‖ r 2 and S θ , r ( φ ) = inf u ∈ H θ r ( Ω ) , ‖ u + φ ‖ L 2 ∗ r

Source: Journal of Elliptic and Parabolic Equations

DOI: 10.1007/s41808-024-00304-5

Authors: Asma Benhamida, Rejeb Hadiji, Habib Yazidi