Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations
نویسنده
چکیده
In this paper, we study fully non-linear elliptic equations in nondivergence form which can be degenerate or singular when “the gradient is small”. Typical examples are either equations involving the m-Laplace operator or Bellman-Isaacs equations from stochastic control problems. We establish an Alexandroff-Bakelman-Pucci estimate and we prove a Harnack inequality for viscosity solutions of such non-linear elliptic equations.
منابع مشابه
Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate fully non-linear elliptic equations
In this paper, we study fully non-linear elliptic equations in nondivergence form which can be degenerate when “the gradient is small”. Typical examples are either equations involving the m-Laplace operator or BellmanIsaacs equations from stochastic control problems. We establish an AlexandroffBakelman-Pucci estimate and we prove a Harnack inequality for viscosity solutions of such degenerate e...
متن کاملNondivergent Elliptic Equations on Manifolds with Nonnegative Curvature
Xavier Cabré Abstra t. We consider a class of second order linear elliptic operators intrinsically defined on Riemannian manifolds, and which correspond to nondivergent operators in Euclidean space. Under the assumption that the sectional curvature is nonnegative, we prove a global Krylov-Safonov Harnack inequality and, as a consequence, a Liouville theorem for solutions of such equations. From...
متن کاملSuper-linear Elliptic Equation for the Pucci Operator without Growth Restrictions for the Data
In this paper we deal with existence and uniqueness of solution to super-linear problems for the Pucci operator: −M(Du) + |u|u = f(x) in IR, where s > 1 and f satisfies only local integrability conditions. This result is well known when, instead of the Pucci operator, the Laplacian or a divergence form operator is considered. Our existence results use the Alexandroff-Bakelman-Pucci inequality s...
متن کاملA New Maximum Principle of Elliptic Differential Equations in Divergence Form
In this paper will be presented a new maximum principle of elliptic differential equations in divergence form which can be regarded as the counterpart of the Alexandroff-Bakelman-Pucci maximum principle of elliptic differential equations in nondivergence form.
متن کاملDiscrete Abp Estimate and Convergence Rates for Linear Elliptic Equations in Non-divergence Form
We design a two-scale finite element method (FEM) for linear elliptic PDEs in non-divergence form A(x) : D2u(x) = f(x). The fine scale is given by the meshsize h whereas the coarse scale is dictated by an integrodifferential approximation of the PDE. We show that the FEM satisfies the discrete maximum principle (DMP) for any uniformly positive definite matrix A(x) provided that the mesh is weak...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017