Abstract In this paper, we analyze an eigenvalue problem for quasi-linear elliptic operators involving homogeneous Dirichlet boundary conditions in a open smooth bounded domain. We show that the eigenfunctions corresponding to eigenvalues belong $$L^{\infty }$$ L ∞ , wh...

We present a finite volume discretization of the nonlinear elliptic problems. The discretization results in a nonlinear algebraic system of equations. A Newton-Krylov algorithm is also presented for solving the system of nonlinear algebraic equations. Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solvin...

We discuss regularity issues for minimizers of three nonlinear elliptic problems. They concern minimal cones, minimizing harmonic maps into a hemisphere, and radial local minimizers of semilinear elliptic equations. We describe the strong analogies among the three regularity theories. They all use a method originated in a paper of J. Simons on the area minimizing properties of cones.