On one variant of strongly nonlinear Gagliardo-Nirenberg inequality involving Laplace operator with application to nonlinear elliptic problems

Agnieszka Kałamajska, Tomasz Choczewski

We obtain the inequality $${\int }_{\Omega }|\nabla u(x){|}^{p}h(u(x))dx\le C(n,p){\int }_{\Omega }{\left(\sqrt{|\Delta u(x)||{\mathcal{T}}_{h,C}(u(x))|}\right)}^{p}h(u(x))dx,$$ where $\Omega \subset {\mathbf{R}}^n$ is a bo…