arXiv subjects

M. L. Carvalho

Publications and source records attributed to M. L. Carvalho.

5 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↗

arXiv2017

The proton radius puzzle

High-precision measurements of the proton radius from laser spectroscopy of muonic hydrogen demonstrated up to six standard deviations smaller values than obtained from electron-proton scattering and hydrogen spectroscopy. The status of this discrepancy, which is known as the proton radius puzzle will be discussed in this paper, complemented with the new insights obtained from spectroscopy of muonic deuterium.

physics.atom-ph↗

arXiv2013

Multiple Positive Solutions for a Class of Nonlinear Elliptic Eigenvalue Problems with a Sign-Changing Nonlinearity

In 2009 Loc and Schmitt established a result on sufficient conditions for multiplicity of solutions of a class of nonlinear eignvalue problems for the p-Laplace operator under Dirichlet boundary conditions, extending an earlier result of 1981 by Peter Hess for the Laplacian. Results on necessary conditions for existence were also established. In the present paper the authors extend the main results by Loc and Schmitt to the $Φ$-Laplacian. To overcome the difficulties with this much more general operator it was necessary to employ regularity results by Lieberman, a strong maximum principle by Pucci and Serrin and a general result on lower and upper solutions by Le.

math.AP↗

arXiv2013

On Variational Multivalued Elliptic Equations on a Bounded Domain in the Presence of Critical Growth

We develop arguments on the critical point theory for locally Lipschitz functionals on Orlicz-Sobolev spaces, along with convexity and compactness techniques to investigate existence of solution of the multivalued equation $\displaystyle - Δ_Φ u \in \partial j(.,u) + λh \mbox{in} Ω$, where $Ω\subset {\bf R}^{N}$ is a bounded smooth domain, $Φ: {\r} \longrightarrow [0,\infty)$ is a suitable N-function, $Δ_Φ$ is the corresponding $Φ$-Laplacian, $λ> 0$ is a parameter, $h:Ω\rightarrow{\r}$ is integrable and $\partial j(., u)$ is the subdifferential of a function $j$ associated with critical growth.

math.AP↗