24 citations · 47 across the 9 of their papers we have counts for
11 papers
An optimal pointwise Morrey-Sobolev inequality
Grey Ercole, Gilberto de Assis Pereira
Let be a bounded, smooth domain of For each we study the optimal function in the pointwise inequality \[ \left\vert v(x)\right\vert…
Torsion functions and the Cheeger problem: a fractional approach
Hamilton Bueno, Grey Ercole, Shirley S. Macedo +1
Let be a Lipschitz bounded domain of , . The fractional Cheeger constant , , is defined by \[h_s(Ω)=\inf_{E\subsetΩ}\frac{P_s(E)}{|E|},\:…
Existence, regularity, asymptotic decay and radiality of solutions to some extension problems
Hamilton Bueno, Aldo H. S. Medeiros, G. A. Pereira
Supposing only that and , for some ,…
On the behavior of least energy solutions of a fractional -Laplacian problem as p goes to infinity
Grey Ercole, Aldo H. S. Medeiros, Gilberto A. Pereira
We study the behavior as of a positive least energy solution of the problem \[ \left\{\begin{array} [c]{lll} \left[ \left( -Δ_{p}\right) ^α+\left( -Δ_…
Pohozaev identities for a pseudo-relativistic Schrödinger operator and applications
H. Bueno, G. A Pereira, A. H. Souza Medeiros
In this paper we prove a Pohozaev-type identity for both the problem in and its harmonic extension to when . So, our s…
Asymptotic behavior of extremals for fractional Sobolev inequalities associated with singular problems
Grey Ercole, Gilberto Assis Pereira, Rémy Sanchis
Let be a smooth, bounded domain of , be a positive, -normalized function, and We study the asymptotic behavior, as o…
Remarks about a generalized pseudo-relativistic Hartree equation
Hamilton Bueno, Olimpio H. Miyagaki, Gilberto A. Pereira
With appropriate hypotheses on the nonlinearity , we prove the existence of a ground state solution for the problem \[(-Δ+m^2)^σu+Vu=\left(W*F(u)\right)f(u)\ \ \text{in }\ \…
Ground state of a magnetic nonlinear Choquard equation
Hamilton Bueno, Guido G. Mamani, Gilberto A. Pereira
We consider the stationary magnetic nonlinear Choquard equation \[-(\nabla+iA(x))^2u+ V(x)u=\bigg(\frac{1}{|x|^α}*F(|u|)\bigg)\frac{f(|u|)}{|u|}{u},\] where $A: \mathbb{R}^{N}\righ…
Asymptotic behavior as of least energy solutions of a -Laplacian problem
Claudianor Alves, Grey Ercole, Gilberto de Assis Pereira
\[ \left\{ \begin{array} [c]{lll} -\left( Δ_{p}+Δ_{q(p)}\right) u=λ_{p}\left\vert u(x_{u})\right\vert ^{p-2}u(x_{u})δ_{x_{u}} & \mathrm{in} & Ω\\ u=0 & \mathrm{on} & \partialΩ, \en…
Fractional Sobolev inequalities associated with singular problems
Grey Ercole, Gilberto de Assis Pereira
In this paper we consider Sobolev inequalities associated with singular problems for the fractional -Laplacian operator in a bounded domain of , .
Asymptotics for the best Sobolev constants and their extremal functions
Grey Ercole, Gilberto de Assis Pereira
Let be a bounded domain of Let, for \[ Λ_{p}(Ω):=\inf\left\{ \left\Vert \nabla u\right\Vert _{p}^{p}:u\in W_{0}^{1,p}(Ω)\quad and\quad\left\V…