Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators
نویسندگان
چکیده
منابع مشابه
Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators
We characterize the validity of the Maximum Principle in bounded domains for fully nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized principal eigenvalue. Here, the maximum principle refers to the property of non-positivity of viscosity subsolutions of the Dirichlet problem. The new notion of generalized principal eigenvalue that we introduce here al...
متن کاملOn Cooperative Elliptic Systems: Principal Eigenvalue and Characterization of the Maximum Principle
The purpose of this set of notes is to present the connection between the classical maximum principle with the principal eigenvalue of the elliptic operator. We will start with the maximum principle for single equations and proceed to the case of cooperative (or weakly-coupled) systems. By adopting an idea due to G. Sweers, we give a characterization of the principal eigenvalue for a cooperativ...
متن کاملA Generalized Maximum Principle for Boundary Value Problems for Degenerate Parabolic Operators with Discontinuous Coefficients
In [14] M.G.Platone Garroni has extended the classical generalized maximum principle (see, for instance, [15]), when the coefficients of the operator are discontinuous, to subsolutions of elliptic linear second order equations with mixed type boundary unilateral conditions, that is, on a portion of the boundary ∂Ω of Ω, the values of the solution are assigned, while on the other part a unilater...
متن کاملGlobal Irregularity for Mildly Degenerate Elliptic Operators
Examples are given of degenerate elliptic operators on smooth, compact manifolds that are not globally regular in C∞. These operators degenerate only in a rather mild fashion. Certain weak regularity results are proved, and an interpretation of global irregularity in terms of the associated heat semigroup is given.
متن کاملAdaptive Eigenvalue Computation for Elliptic Operators
This article is concerned with recent developments of adaptive wavelet solvers for elliptic eigenvalue problems. We describe the underlying abstract iteration scheme of the preconditioned perturbed iteration. We apply the iteration to a simple model problem in order to identify the main ideas which a numerical realization of the abstract scheme is based upon. This indicates how these concepts c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2015
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2014.10.012