Mathematical Sciences: Semilinear Partial Differential Equations and Quasilinear Variational Inequalities

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This project will consider existence, regularity, local and global behavior, and symmetry of solutions to nonlinear elliptic equations and variational inequalities. Particular emphasis will be placed on semilinear elliptic equations in the open space, scalar curvature equations, and variational inequalities. These problems come from questions in pure and applied mathematics. The results are of interests to fields ranging from diffential geometry to lubrication.