The main goal of this project is to develop new methods of nonlinear potential theory, harmonic analysis, and partial differential equations applicable to a wide class of quasilinear and fully nonlinear elliptic equations. Existence of solutions understood in the renormalized or viscosity sense, sharp integral and pointwise estimates of solutions, and removable singularities will be studied. A related part of this project is concerned with nonlinear integral inequalities for Wolff's potentials, as well as inequalities with indefinite weights which appear in the form boundedness problem for linear partial differential operators with distributional coefficients.

The proposed research will establish new applications to various problems of nonlinear science, harmonic analysis, operator theory, and mathematical physics which are widely used in the studies of heat transfer, fluid flow, quantum theory, control theory, and stochastic processes. The broader impact will result in further advances in understanding of basic nonlinear phenomena in applied mathematics, physics, environmental and technological sciences which may be useful in teaching and training of graduate students, younger mathematicians and applied scientists.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
0556309
Program Officer
Bruce P. Palka
Project Start
Project End
Budget Start
2006-06-01
Budget End
2011-05-31
Support Year
Fiscal Year
2005
Total Cost
$142,380
Indirect Cost
Name
University of Missouri-Columbia
Department
Type
DUNS #
City
Columbia
State
MO
Country
United States
Zip Code
65211