Manuel del Pino

most citedEntire Solutions of the Allen-Cahn equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in

R^{3}

14 citations · 27 across the 2 of their papers we have counts for

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math.AP2009★ 14 cited

Entire Solutions of the Allen-Cahn equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in $R^{3}$

Manuel del Pino, Mike Kowalczyk, Juncheng Wei

We consider minimal surfaces $M$ which are complete, embedded and have finite total curvature in $R^{3}$ , and bounded, entire solutions with finite Morse index of the Allen-Cahn equ…

math.AP2008★ 13 cited

On De Giorgi Conjecture in Dimension $N \geq 9$

Manuel del Pino, Mike Kowalczyk, Juncheng Wei

A celebrated conjecture due to De Giorgi states that any bounded solution of the equation $Δ u + (1 - u^{2}) u = 0in R^{N}$ with $\pp_{y_N}u >0$ must be such that its level sets…

math.AP2006

The two-dimensional Lazer-McKenna conjecture for an exponential nonlinearity

Manuel del Pino, Claudio Muñoz

We consider the problem of Ambrosetti-Prodi type \begin{equation}\label{0}\quad\begin{cases} Δu + e^u = sϕ_1 + h(x) &\hbox{in} Ω, u=0 & \hbox{on} \partial Ω, \end{cases} \nonumber…

Entire Solutions of the Allen-Cahn equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in R3

On De Giorgi Conjecture in Dimension N≥9

The two-dimensional Lazer-McKenna conjecture for an exponential nonlinearity

Entire Solutions of the Allen-Cahn equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in $R^{3}$

On De Giorgi Conjecture in Dimension $N \geq 9$