This project will focus primarily on problems arising in the theory of elliptic partial differential equations. They are motivated to some extent by considerations of quasiregular mappings in n-dimensional Euclidean space. These are considered as natural extensions to higher dimension of classical analytic function theory. In addition, solutions of quasilinear elliptic partial differential equations replace harmonic functions. The conformally invariant extension to n-dimensions of the Laplace operator is the so-called N-Laplacian. Work will be done in seeking conditions on bounded weak solutions of quasilinear equations to have gradients of bounded mean oscillation. Even in the linear case this question is still open. Estimates on the oscillation of boundary values of the gradient will be sought. Another line of investigation will focus on the existence of branched quasiregular maps. When the maps are sufficiently smooth, no branching occurs. The minimal smoothness assumptions are not known. Finally, studies will be made of parabolic divergence type equations to establish whether Holder continuity can be expected of bounded weak solutions. This work is related to research in conformal geometry and potential theory.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
8703286
Program Officer
John V. Ryff
Project Start
Project End
Budget Start
1987-07-15
Budget End
1988-12-31
Support Year
Fiscal Year
1987
Total Cost
$6,688
Indirect Cost
Name
Purdue University
Department
Type
DUNS #
City
West Lafayette
State
IN
Country
United States
Zip Code
47907