New Maximum Principles for Linear Elliptic Equations
نویسندگان
چکیده
We prove extensions of the estimates of Aleksandrov and Bakel′man for linear elliptic operators in Euclidean space R to inhomogeneous terms in L spaces for q < n. Our estimates depend on restrictions on the ellipticity of the operators determined by certain subcones of the positive cone. We also consider some applications to local pointwise and L estimates.
منابع مشابه
New variants of the global Krylov type methods for linear systems with multiple right-hand sides arising in elliptic PDEs
In this paper, we present new variants of global bi-conjugate gradient (Gl-BiCG) and global bi-conjugate residual (Gl-BiCR) methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. It is shown that these new algorithms converge faster and more smoothly than the Gl-...
متن کاملMaximum Principles for a Class of Nonlinear Second Order Elliptic Differential Equations
In this paper we investigate maximum principles for functionals defined on solutions to special partial differential equations of elliptic type, extending results by Payne and Philippin. We apply such maximum principles to investigate one overdetermined problem.
متن کاملStrong Maximum Principles for Anisotropic Elliptic and Parabolic Equations
We investigate vanishing properties of nonnegative solutions of anisotropic elliptic and parabolic equations. We describe the optimal vanishing sets, and we establish strong maximum principles.
متن کاملDuality Principles for Fully Non- linear Elliptic Equations
In this paper we use duality theory to associate certain measures to fully-nonlinear elliptic equations. These measures are the natural extension of the Mather measures to controlled stochastic processes and associated second-order elliptic equations. We apply these ideas to prove new a-priori estimates for smooth solutions of fully nonlinear elliptic equations. Supported in part by FCT/POCTI/F...
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 کامل