Bergman operators for elliptic equations in three independent variables

Complex Variables and Elliptic Equations

A sharp Hölder estimate for elliptic equations in two variables

We prove a sharp Hölder estimate for solutions of linear two-dimensional, divergence form elliptic equations with measurable coefficients, such that the matrix of the coefficients is symmetric and has unit determinant. Our result extends some previous work by Piccinini and Spagnolo [7]. The proof relies on a sharp Wirtinger type inequality.

Evolution Equations Governed by Elliptic Operators

Hierarchical Interpolative Factorization for Elliptic Operators: Integral Equations

This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions. This factorization takes the form of an approximate generalized LU decomposition that permits the efficient application of the discretized operator and its inverse. HIF-IE is based on the recursive skeletonization algorithm but incorpo...

Hierarchical Interpolative Factorization for Elliptic Operators: Differential Equations

This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization takes the form of an approximate generalized LU/LDL decomposition that facilitates the efficient inversion of the discretized operator. HIF-DE is based on the nested dissection multifrontal method but uses skeletonizati...