# 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}
}
• Published 1997
• Physics
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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#### References

SHOWING 1-10 OF 12 REFERENCES
The problem of dirichlet for quasilinear elliptic differential equations with many independent variables
• J. Serrin
• Mathematics
• Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
• 1969