New maximum principles for linear elliptic equations

2006/07/10 by Hung-Ju Kuo, Hung‐Ju Kuo, Kuo, Hung-Ju +2 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #math.AP #msc:35J15

paper · pdf · doi:10.48550/arxiv.math/0607240

arxiv created 2006/07/10 · arxiv updated 2009/12/01

Abstract

We prove extensions of the estimates of Aleksandrov and Bakel'man for linear elliptic operators in Euclidean space ℝ^{\it n} to inhomogeneous terms in L^q 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 L² estimates.

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