New maximum principles for linear elliptic equations

Hung Ju Kuo; Neil S. Trudinger

doi:10.1512/iumj.2007.56.3073

New maximum principles for linear elliptic equations

Hung Ju Kuo^*, Neil S. Trudinger

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	2439-2452
Number of pages	14
Journal	Indiana University Mathematics Journal
Volume	56
Issue number	5
DOIs	https://doi.org/10.1512/iumj.2007.56.3073
Publication status	Published - 2007

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10.1512/iumj.2007.56.3073

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title = "New maximum principles for linear elliptic equations",

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",

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AU - Kuo, Hung Ju

AU - Trudinger, Neil S.

PY - 2007

Y1 - 2007

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AB - 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

KW - Green's function

KW - K-Hessian operator

KW - Linear elliptic equations

KW - Local estimates

KW - Maximum principles

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U2 - 10.1512/iumj.2007.56.3073

DO - 10.1512/iumj.2007.56.3073

M3 - Article

SN - 0022-2518

VL - 56

SP - 2439

EP - 2452

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 5

ER -

New maximum principles for linear elliptic equations

Abstract

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