# Elliptic Partial Differential Equations of Second Order

@inproceedings{Bassanini1997EllipticPD, title={Elliptic Partial Differential Equations of Second Order}, author={P. Bassanini and A. Elcrat}, year={1997} }

We study in this chapter a class of partial differential equations that generalize and are to a large extent represented by Laplace’s equation. These are the elliptic partial differential equations of second order. A linear partial differential operator L defined by
$$ Lu{\text{: = }}{a_{ij}}\left( x \right){D_{ij}}u + {b_i}\left( x \right){D_i}u + c\left( x \right)u $$
is elliptic on Ω ⊂ ℝ n if the symmetric matrix [a ij ] is positive definite for each x ∈ Ω. We have used the notation D… Expand

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