On pseudomonotone elliptic operators with functional dependence on unbounded domains

Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

Elliptic and parabolic problems in unbounded domains

We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi-explicit representation formulas via operatorvalued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the larg...

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 Morse Index Theorem for Elliptic Operators on Bounded Domains

We consider a second-order, selfadjoint elliptic operator L on a smooth one-parameter family of domains {Ωt}t∈[a,b] with no assumptions on the geometry of the Ωt’s. It is shown that the Morse index of L can be equated with the Maslov index of an appropriately defined path in a symplectic Hilbert space constructed on the boundary of Ωb. Our result is valid for a wide variety of boundary conditio...

L^p-Regularity for Elliptic Operators with Unbounded Coefficients