Maximum principles for parabolic equations

Higher regularity for parabolic equations and maximum principles

Strong 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.

Invariance Principles for Parabolic Equations with Random Coeecients Invariance Principles for Parabolic Equations with Random Coeecients

A general Hilbert-space-based stochastic averaging theory is brought forth in this note for arbitrary-order parabolic equations with (possibly long range dependent) random coeecients. We start with regularity conditions on the coeecients and Cauchy data of @ t u " (x; t) = X 0jkjj2p A k (x; t="; !)@ k x u " (x; t); u " (x; 0) = '(x) (1) which are only slightly stronger than those required to pr...

Discrete maximum principles for nonlinear parabolic

Discrete maximum principles are established for finite element approximations 10 of nonlinear parabolic PDE systems with mixed boundary and interface conditions. The 11 results are based on an algebraic discrete maximum principle for suitable ODE systems. 12

New Maximum Principles for Linear Elliptic Equations

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.