3 papers
math.AP2025
Critical equations with a sharp change of sign in the nonlinearity
Mónica Clapp, Jorge Faya, Alberto Saldaña
We establish the existence and nonexistence of entire solutions to a semilinear elliptic problem whose nonlinearity is the critical power multiplied by a function that takes the va…
math.AP2025
Concentration on the Boundary and Sign-Changing Solutions for a Slightly Subcritical Biharmonic Problem
Salomón Alarcón, Jorge Faya, Carolina Rey
We consider the fourth-order nonlinear elliptic problem: \begin{equation*} \begin{array}{ll} Î(a(x)Îu) = a(x) \left\vert u \right\vert^{p-2-ε} u \ \text{ in } \ Ω, \hspace{0.6c…
math.AP2024
Optimal pinwheel partitions for the Yamabe equation
Mónica Clapp, Jorge Faya, Alberto Saldaña
We establish the existence of an optimal partition for the Yamabe equation in the whole space made up of mutually linearly isometric sets, each of them invariant under the action o…