Linear elliptic partial differential equations can be characterized as those whose principal symbol is nowhere zero.

His research is in the field of nonlinear partial differential equations, primarily elliptic equations.

This means that one can solve linear elliptic differential equations more or less explicitly by using the theory of pseudo-differential operators.

To ensure non-divergence of the flow field, an elliptic equation is solved.

Yet it can be shown for a very large class of degenerate elliptic equations.

The equations for an individual slice are elliptic partial differential equations.

The elliptic sinh-Gordon equation may be defined in a similar way.

The result is of particular importance in the theory of elliptic partial differential equations.

He was among the first scientists to study elliptic and parabolic equations with discontinuous coefficients.

Thus it cannot be used directly on purely elliptic equations, such as Laplace's equation.