New maximum principles for linear elliptic equations
Hung-ju KuoNeil Trudinger
35J15maximum principleslinear elliptic equations$k$-Hessian operatorGreen's functionlocal estimates
We prove extensions of the estimates of Aleksandrov and Bakel'man for linear elliptic operators in Euclidean space $\mathbb{R}^n$ 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 $L^2$ estimates.
Indiana University Mathematics Journal
2007
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10.1512/iumj.2007.56.3073
10.1512/iumj.2007.56.3073
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Indiana Univ. Math. J. 56 (2007) 2439 - 2452
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