C. Bernardini

most citedBoundary value problems for Choquard equations

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math.AP2023★ 1 cited

Boundary value problems for Choquard equations

Chiara Bernardini, Annalisa Cesaroni

We prove existence of a positive radial solution to the Choquard equation $- Δ u + V u = (I_{α} * ∣ u ∣^{p}) ∣ u ∣^{p - 2} u in Ω$ with Neumann or Dirichlet boundary conditions…

math.AP2023

Existence and compactness of conformal metrics on the plane with unbounded and sign-changing Gaussian curvature

Chiara Bernardini

We show that the prescribed Gaussian curvature equation in $R^{2}$ $- Δ u = (1 - ∣ x ∣^{p}) e^{2 u},$ has solutions with prescribed total curvature equal to $Λ:=\int_{\mathbb{R}^2}(…

math.AP2022

Mass concentration for Ergodic Choquard Mean-Field Games

Chiara Bernardini

We study concentration phenomena in the vanishing viscosity limit for second-order stationary Mean-Field Games systems defined in the whole space $R^{N}$ with Riesz-type agg…