arXiv subjects
Publications and source records attributed to N. Saintier.
We find interpretation using optimal mass transport theory for eigenvalue problems obtained as limits of the eigenvalue problems for the fractional $p-$Laplacian operators as $p\to +\infty$. We deal both with Dirichlet and Neumann boundary conditions.
In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality $S\|u\|^p_{L^{p_*}(\partialΩ) \hookrightarrow \|u\|^p_{W^{1,p}(Ω)}$ that are independent of $Ω$. This estimates generalized those of [3] for general $p$. Here $p_* := p(N-1)/(N-p)$ is the critical exponent for the immersion and $N$ is the space dimension. Then we apply our results first to prove existence of positive solutions to a nonlinear elliptic problem with a nonlinear boundary condition with critical growth on the boundary, generalizing the results of [16]. Finally, we study an optimal design problem with critical exponent.