9 citations · 40 across the 18 of their papers we have counts for
4 papers · 1 filter
The critical dimension for a fourth order elliptic problem with singular nonlinearity
Craig Cowan, Pierpaolo Esposito, Nassif Ghoussoub
We study the regularity of the extremal solution of the semilinear biharmonic equation $\bi u=\fλ{(1-u)^2}$, which models a simple Micro-Electromechanical System (MEMS) device on a…
Regularity of the extremal solution in a MEMS model with advection
Nassif Ghoussoub, Craig Cowan
We consider the regularity of the extremal solution of the nonlinear eigenvalue problem (S)_λ\qquad {rcr} -Δu + c(x) \cdot \nabla u &=& \fracλ{(1-u)^2} \qquad {in }, u &=& 0 \q…
Uniqueness of solutions for an elliptic equation modeling MEMS
Nassif Ghoussoub, Pierpaolo Esposito
We study the effect of the parameter , the dimension , the profile and the geometry of the domain , on the question of uniqueness of the solutions t…
A variational theory for monotone vector fields
Nassif Ghoussoub
Monotone vector fields were introduced almost 40 years ago as nonlinear extensions of positive definite linear operators, but also as natural extensions of gradients of convex pote…