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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…