New maximum principles for linear elliptic equations

Kuo, Hung Ju; Trudinger, Neil S.

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New maximum principles for linear elliptic equations

Date

2007

Authors

Kuo, Hung Ju

Trudinger, Neil S.

Abstract

We prove extensions of the estimates of Aleksandrov and Bakel'man for linear elliptic operators in Euclidean space ℝn to inhomogeneous terms in Lq 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. Indiana University Mathematics Journal