4 papers · 1 filter
Trace and Hardy-Sobolev type inequalities and applications to a quasilinear elliptic problem in half-space
Loïc Constantin, Ranieri França Freire, Jacques Giacomoni
In the present paper we are dealing with the following quasilinear elliptic problem: \begin{equation*} \begin{cases} -\mathrm{div}(Ï(x_N) |\nabla u|^{p-2}\nabla u) =a|u|^{s-2}u &\…
Logistic elliptic and parabolic problem for the fractional -Laplacian
Loïc Constantin, Carlos Alberto Santos, Guillaume Warnault
In this paper we prove existence, uniqueness of weak solutions of the following nonlocal nonlinear logistic equation \begin{equation*} \begin{cases} (-Î)_p^s u_λ=λu_λ^q - b(x)u…
Doubly nonlinear parabolic equation involving a mixed local-nonlocal operator and a convection term
Loïc Constantin, Carlota M. Cuesta
In this paper we study a doubly degenerate parabolic equation involving a convection term and the operator which is a linear combination o…
Existence and global behaviour of solutions of a parabolic problem involving the fractional -Laplacian in porous medium
Loïc Constantin, Jacques Giacomoni, Guillaume Warnault
In this paper, we prove the existence and the uniqueness of a weak and mild solution of the following nonlinear parabolic problem involving the porous -fractional Laplacian: \be…