1 citations · 3 across the 14 of their papers we have counts for
15 papers
A nonlinear problem related to optimal insulation
Genival da Silva
We study a generalization of the classical optimal insulation problem by replacing the standard Laplacian with the \ti{p-Laplacian}, leading to a \ti{p-Poisson equation} with Robin…
A -Laplacian Schrödinger--Maxwell system with rapidly growing nonlinearities
Genival da Silva
Let , , be a bounded domain and let . Inspired by the exponential case treated in \cite{BO2026}, we study the quasilinear Schrödinger--Maxwell syst…
An equation involving the 1-Laplacian and a singular nonlinearity
Genival da Silva
We prove existence of solutions to a nonlinear degenerate elliptic equation of the form \[ \begin{cases} -Δ_{1} u+ \frac{|D u|}{(1-u)^γ}=g & \mbox{in ,}\\ u=0 \hfill & \mbox{on…
An elliptic equation with power nonlinearity and degenerate coercivity
Genival da Silva
We discuss the existence and regularity of solutions to the following Dirichlet problem: $$\begin{equation} \begin{cases} -\textrm{div}\left(\frac{Du}{(1+|u|)^θ}\right)= -\textrm{d…
An inhomogeneous p-laplacian equation with a Hardy potential
Genival da Silva
In this work we study the existence and regularity of solutions to the following equation: where and , wh…
Quasi-linear elliptic equations with superlinear convection
Genival da Silva
We discuss the existence and regularity of solutions to a quasi-linear elliptic equation involving a Leray-Lions operator and a convection term with superlinear growth. In particul…
On a fully nonlinear k-Hessian system of Lane-Emden type
Genival da Silva
In this manuscript we prove the existence of solutions to a fully nonlinear system of (degenerate) elliptic equations of Lane-Emden type and discuss a inhomogeneous generalization.
Radially symmetric solutions to a Lane-Emden type system
Genival da Silva
The existence of radially symmetric solutions is discussed for a Lane-Emden type system. This answer a question posed by da Silva and do O (2024). We also comment on the inhomogene…
Notes on continuous weak solutions to the ideal Hall equation
Genival da Silva
Using convex integration, we construct continuous weak solutions to the ideal Hall equation with a given energy profile. This is a first step in the direction of proving the Onsage…
Known cases of the Hodge conjecture
Genival da Silva
The Hodge conjecture is a major open problem in complex algebraic geometry. In this survey, we discuss the main cases where the conjecture is known, and also explain an approach by…
Notes on the Hodge Conjecture for Fermat Varieties
Genival da Silva
We review a combinatoric approach to the Hodge Conjecture for Fermat Varieties and announce new cases where the conjecture is true.
On the Topology of Fano Smoothings
Tom Coates, Alessio Corti, Genival da Silva
Suppose that X is a Fano manifold that corresponds under Mirror Symmetry to a Laurent polynomial f, and that P is the Newton polytope of f. In this setting it is expected that ther…
On the monodromy of elliptic surfaces
Genival da Silva
There have been several constructions of family of varieties with exceptional monodromy group. In most cases, these constructions give Hodge structures with high weight(Hodge numbe…
On the arithmetic of Landau-Ginzburg model of a certain class of threefolds
Genival Da Silva
We prove that the Apery constants for a certain class of Fano threefolds can be obtained as a special value of a higher normal function.
Arithmetic of degenerating principal variations of Hodge structure: examples arising from mirror symmetry and middle convolution
Genival da Silva, Matt Kerr, Gregory Pearlstein
We collect evidence in support of a conjecture of Griffiths, Green and Kerr on the arithmetic of extension classes of limiting mixed Hodge structures arising from semistable degene…