We study the appropriate versions of parabolicity stochastic completeness and related Liouville properties for a general class of operators which include the p-Laplace operator, and the non linear singular operators in non-diagonal form considered by J. Serrin and collaborators.
Per una classe di operatori pseudodifferenziali a caratteristiche multiple vengono date condizioni necessarie e sufficienti per la validità di stime dal basso «ottimali»
We obtain a maximum principle at infinity for solutions of a class of nonlinear singular elliptic differential inequalities on Riemannian manifolds under the sole geometrical assumptions of volume growth conditions. In the case of the Laplace-Beltrami operator we relate our results to stochastic completeness and parabolicity of the manifold.
The aim of the first part of a series of papers is to give a description of invariant differential operators on manifolds with an almost Hermitian symmetric structure of the type which are defined on bundles associated to the reducible but undecomposable representation of the parabolic subgroup of the Lie group . One example of an operator of this type is the Penrose’s local twistor transport. In this part general theory is presented, and conformally invariant operators are studied in more...
The spectrum of the Laplacian on manifolds with cylindrical ends consists of continuous spectrum of locally finite multiplicity and embedded eigenvalues. We prove a Weyl-type asymptotic formula for the sum of the number of embedded eigenvalues and the scattering phase. In particular, we obtain the optimal upper bound on the number of embedded eigenvalues less than or equal to , where is the dimension of the manifold.