maximum principle

Morse index and symmetry for elliptic problems with nonlinear mixed boundary conditions

We consider an elliptic problem of the type where Ω is a bounded Lipschitz domain in ℝ N with a cylindrical symmetry, ν stands for the outer normal and. Under a Morse index condition, we prove cylindrical symmetry results for solutions of the above problem.

Elliptic partial differential equations of second order (book review)

This book is the reprint of the 1998 edition of Elliptic Partial Differential Equations of Second Order by David Gilbarg and Neil S. Trudinger that originally appeared in 1977.