arXiv subjects

E. D. Silva

Publications and source records attributed to E. D. Silva.

3 recordsLinked to original sources

arXiv2021

Regularity results for quasilinear elliptic problems driven by the fractional $Φ$-Laplacian operator

It is established $L^{p}$ estimates for the fractional $Φ$-Laplacian operator defined in bounded domains where the nonlinearity is subcritical or critical in a suitable sense. Furthermore, using some fine estimates together with the Moser's iteration, we prove that any weak solution for fractional $Φ$-Laplacian operator defined in bounded domains belongs to $L^\infty(Ω)$ under appropriate hypotheses on the $N$-function $Φ$. Using the Orlicz space and taking into account the fractional setting for our problem the main results are stated for a huge class of nonlinear operators and nonlinearities.

math.AP↗

arXiv2018

Revised regularity results for quasilinear elliptic problems driven by the $Φ$-Laplacian operator

It is establish regularity results for weak solutions of quasilinear elliptic problems driven by the well known $Φ$-Laplacian operator given by \begin{equation*} \left\{\ \begin{array}{cl} \displaystyle-Δ_Φu= g(x,u), & \mbox{in}~Ω, u=0, & \mbox{on}~\partial Ω, \end{array} \right. \end{equation*} where $Δ_Φu :=\mbox{div}(ϕ(|\nabla u|)\nabla u)$ and $Ω\subset\mathbb{R}^{N}, N \geq 2,$ is a bounded domain with smooth boundary $\partialΩ$. Our work concerns on nonlinearities $g$ which can be homogeneous or non-homogeneous. For the homogeneous case we consider an existence result together with a regularity result proving that any weak solution remains bounded. Furthermore, for the non-homogeneous case, the nonlinear term $g$ can be subcritical or critical proving also that any weak solution is bounded. The proofs are based on Moser's iteration in Orclicz and Orlicz-Sobolev spaces.

math.AP↗

arXiv2016

Sign changing solutions for quasilinear superlinear elliptic problems

Results on existence and multiplicity of solutions for a nonlinear elliptic problem driven by the $Φ$-Laplace operator are established. We employ minimization arguments on suitable Nehari manifolds to build a negative and a positive ground state solutions. In order to find a nodal solution we employ additionally the well known Deformation Lemma and Topological Degree Theory.

math.AP↗