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Uniformly Elliptic Equations in Nondivergence Form

  • Cristian E. Gutiérrez
Chapter
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Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 89)

Abstract

In this chapter we consider linear operators of the form
$$\displaystyle{Lu =\sum _{ i,j=1}^{n}a_{ ij}(x)D_{ij}u(x)}$$
where the coefficient matrix A(x) = (a ij (x)) is symmetric and uniformly elliptic, that is
$$\displaystyle{\lambda \vert \xi \vert ^{2} \leq \langle A(x)\xi,\xi \rangle \leq \Lambda \vert \xi \vert ^{2},}$$
for all \(\xi \in \mathbb{R}^{n}\) and \(x \in \Omega \subset \mathbb{R}^{n}.\)

Keywords

Linear Operator Elliptic Equation Coefficient Matrix Elliptic Operator Critical Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Cristian E. Gutiérrez
    • 1
  1. 1.Department of MathematicsTemple UniversityPhiladelphiaUSA

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