Abd-Elhameed, "Accurate spectral solutions for the parabolic and elliptic partial differential equations
by the ultraspherical tau method," Journal of Computational and Applied Mathematics, vol.
of Minnesota) investigates divergence-form elliptic partial differential equations
in two-dimensional Lipschiz domains whose coefficient matrices have small (but possibly non-zero) imaginary parts, and depend only on one of the two coordinates.
After consideration of basic ideas such as surgery, quadric transformations, infinitesimal deformations, and deformations, chapters discuss sheaf cohomology and completeness theorems, proofs of de Rham and Dolbeault theorems, Kahler manifolds and the Kodair embedding theorem, and the theory of elliptic partial differential equations
as it applies to semi-continuity theorems and Kuranishi's theorem.
They look at the most important variational methods for those elliptic partial differential equations
that are described by non-homogeneous differential operators and that contain one or more power-type non-linearities with variable exponents.
Nadirashvili, Tkachev, and Vladut present students, academics, and mathematicians with a collection of applications of noncommutative and nonassociative algebras, used to construct unusual solutions to nonlinear elliptic partial differential equations
of the second order.