Mathematical Sciences: On Nonlinear Elliptic Equations and Systems

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This project will involve various problems in the calculus of variations related to the existence and regularity of solutions of differential equations. The first problem deals with the equations of uniform rotations of selfgravitating stars. The work builds on recent work by the investigator. The second problem deals with elliptic equations with critical exponent. Here relations between solvability and geometry of domains will be studied. Finally, the regularity of minimizers of degenerate elliptic integrals will be considered. These studies are part of the theoretical basis of mathematical physics in areas such as celestial mechanics and material sciences.