5 papers
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 &\…
A matrix-based spectral method for the numerical approximation of the fractional Laplacian and the fractional -Laplacian of functions defined on
Loïc Constantin, Carlota M. Cuesta, Francisco de la Hoz
Given a function defined on , its fractional -Laplacian is given by $$(-Î)_p^su(\vec x)=C_1(n,s,p)\int_{\mathbb R^n}\frac{|u(\vec x)-u(\vec y)|^{p-2}(u(\vec x)…
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…