Normalized Eigenvectors for Nonlinear Abstract and Elliptic Operators

3 Spin Operators and Eigenvectors

Symmetry Results for Nonlinear Elliptic Operators with Unbounded Drift

We prove the one-dimensional symmetry of solutions to elliptic equations of the form −div(ea(|∇u|)∇u) = f(u)e, under suitable energy conditions. Our results hold without any restriction on the dimension of the ambient space.

A nonlinear spectral theorem for abstract Nemitsky operators

Liouville Properties and Critical Value of Fully Nonlinear Elliptic Operators

We prove some Liouville properties for suband supersolutions of fully nonlinear degenerate elliptic equations in the whole space. Our assumptions allow the coefficients of the first order terms to be large at infinity, provided they have an appropriate sign, as in OrnsteinUhlenbeck operators. We give two applications. The first is a stabilization property for large times of solutions to fully n...

A Degree Theory for Second Order Nonlinear Elliptic Operators with Nonlinear Oblique Boundary Conditions

In this paper we introduce an integer-valued degree for second order fully nonlinear elliptic operators with nonlinear oblique boundary conditions. We also give some applications to the existence of solutions of certain nonlinear elliptic equations arising from a Yamabe problem with boundary and reflector problems.