On a linear second order degenerate elliptic equation.
On existence of a unique generalized solution to systems of elliptic PDEs at resonance
The Dirichlet boundary value problem for systems of elliptic partial differential equations at resonance is studied. The existence of a unique generalized solution is proved using a new min-max principle and a global inversion theorem.
On Lyapunov-type inequalities for two-dimensional nonlinear partial systems.
On phase segregation in nonlocal two-particle Hartree systems
We prove the phase segregation phenomenon to occur in the ground state solutions of an interacting system of two self-coupled repulsive Hartree equations for large nonlinear and nonlocal interactions. A self-consistent numerical investigation visualizes the approach to this segregated regime.
On the Neumann problem for systems of elliptic equations involving homogeneous nonlinearities of a critical degree
We establish the existence of solutions for the Neumann problem for a system of two equations involving a homogeneous nonlinearity of a critical degree. The existence of a solution is obtained by a constrained minimization with the aid of P.-L. Lions' concentration-compactness principle.
Optimal interior partial regularity for nonlinear elliptic systems for the case under natural growth condition.