Invariant elliptic estimates

Estimates on invariant tori near an elliptic equilibrium point of a Hamiltonian system

We give a precise statement for KAM theorem in a neighbourhood of an elliptic equilib rium point of a Hamiltonian system If the frequencies of the elliptic point are nonresonant up to a certain order K and a nondegeneracy condition is ful lled we get an estimate for the measure of the complement of the KAM tori in a neighbourhood of given radius Moreover if the frequencies satisfy a Diophantine...

Dimension Estimates for Invariant Setsof

Degenerate Conformally Invariant Fully Nonlinear Elliptic Equations

There has been much work on conformally invariant fully nonlinear elliptic equations and applications to geometry and topology. See for instance [17], [5], [4], [10], [14], [9], and the references therein. An important issue in the study of such equations is to classify entire solutions which arise from rescaling blowing up solutions. Liouville type theorems for general conformally invariant fu...

Invariant Measures Associated to Degenerate Elliptic Operators

This paper is devoted to the study of the existence and uniqueness of the invariant measure associated to the transition semigroup of a diffusion process in a bounded open subset of Rn. For this purpose, we investigate first the invariance of a bounded open domain with piecewise smooth boundary showing that such a property holds true under the same conditions that insure the invariance of the c...

Estimates for Eigenvalues of Quasilinear Elliptic

In this paper we find explicit lower bounds for Dirichlet eigenvalues of a weighted quasilinear elliptic system of resonant type in terms of the eigenvalues of a single p-Laplace equation. Also we obtain asymptotic bounds by studying the spectral counting function which is defined as the number of eigenvalues smaller than a given value.