Elliptic operators with unbounded diffusion, drift and potential terms

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.

Boundary value problems for elliptic operators with singular drift terms

Let Ω be a Lipschitz domain in R, n ≥ 3, and L = divA∇ − B∇ be a second order elliptic operator in divergence form with real coefficients such that A is a bounded elliptic matrix and the vector field B ∈ Lloc(Ω) is divergence free and satisfies the growth condition dist(X, ∂Ω)|B(X)| ≤ ε1 for ε1 small in a neighbourhood of ∂Ω. For these elliptic operators we will study on the basis of the theory...

L^p-Regularity for Elliptic Operators with Unbounded Coefficients

The Dirichlet Problem for Elliptic Equations with Drift Terms

We establish absolute continuity of the elliptic measure associated to certain second order elliptic equations in either divergence or nondivergence form, with drift terms, under minimal smoothness assumptions on the coefficients.

Neumann Problems with Indefinite and Unbounded Potential and Concave Terms

We consider a semilinear parametric Neumann problem driven by the negative Laplacian plus an indefinite and unbounded potential. The reaction is asymptotically linear and exhibits a negative concave term near the origin. Using variational methods together with truncation and perturbation techniques and critical groups, we show that for all small values of the parameter the problem has at least ...