Degenerate Elliptic Systems

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Degenerate elliptic resonances

Quasi-periodic motions on invariant tori of an integrable system of dimension smaller than half the phase space dimension may continue to exists after small perturbations. The parametric equations of the invariant tori can often be computed as formal power series in the perturbation parameter and can be given a meaning via resummations. Here we prove that, for a class of elliptic tori, a resumm...

on the spectral properties of degenerate non-selfadjoint elliptic systems of differential operators

Degenerate elliptic equations with singular nonlinearities

The behavior of the “minimal branch” is investigated for quasilinear eigenvalue problems involving the p-Laplace operator, considered in a smooth bounded domain of RN , and compactness holds below a critical dimension N #. The nonlinearity f (u) lies in a very general class and the results we present are new even for p = 2. Due to the degeneracy of p-Laplace operator, for p = 2 it is crucial to...

Degenerate elliptic operators in one dimension

Let H be the symmetric second-order differential operator on L2(R) with domain C c (R) and action Hφ = −(c φ ) where c ∈ W 1,2 loc (R) is a real function which is strictly positive on R\{0} but with c(0) = 0. We give a complete characterization of the self-adjoint extensions and the submarkovian extensions of H . In particular if ν = ν+ ∨ ν− where ν±(x) = ± ∫ ±1 ±x c then H has a unique self-ad...