Existence and Estimates of Solutions for Various Elliptic Equation Models

Abstract

The thesis is devoted to studying the existence and estimates of solutions for various elliptic equations. We establish the partial Schauder estimates to a sub-elliptic equation by using a new estimate of the Newton potential. By using the truncated technique we establish the sufficient condition for the existence of the solution to a nonlinear elliptic equation with negative exponent. A new variational functional is developed to study a 2-dimensional Minkowski problem.