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math.AP2026
Positive Solutions for an Indefinite-Weight Minkowski Mean Curvature Neumann Problem: Multiplicity and Asymptotic Behaviour
Ricardo Ziegele
We study the Neumann boundary value problem $$ -\operatorname{div}\left(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\right) = λa(x)g(u) \quad \text{in } Ω, \qquad \frac{\nabla u}{\sqrt{1…
math.AP2026
Positive and nodal solutions for the Minkowski mean curvature equation: multiplicity and asymptotics
Alberto Boscaggin, Francesca Colasuonno, Ricardo Ziegele
We consider the Dirichlet problem for the mean curvature operator in Minkowski space, \[ -\operatorname{div}\left(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\right) = λu + μh(x,u) \quad…
math.AP2025
Existence and a priori bounds for fully nonlinear PDEs with a harmonic map-like structure
Gabrielle Nornberg, Ricardo Ziegele
In this paper, we study a new class of fully nonlinear uniformly elliptic equations with a so-called harmonic map-like structure, whose model case is given by \begin{equation*} \ma…