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Qualitative Properties Of Solutions Of Fully Nonlinear Equations And Overdetermined Problems, Jiuyi Zhu
Qualitative Properties Of Solutions Of Fully Nonlinear Equations And Overdetermined Problems, Jiuyi Zhu
Wayne State University Dissertations
In section 2 of part I, We study the maximum principles and radial symmetry for viscosity solutions of fully nonlinear partial differential equations. We
obtain the radial symmetry and monotonicity properties for
nonnegative viscosity solutions of fully nonlinear equations under some asymptotic decay rate at infinity. Our symmetry and monotonicity results also
apply to Hamilton-Jacobi-Bellman or Isaccs equations. A new maximum
principle for viscosity solutions to fully nonlinear elliptic equations is established. In section 3, We establish Liouville-type theorems and decay estimates for viscosity solutions to a class of fully nonlinear elliptic equations or systems in half spaces without the …