On a 2D vector Poisson problem with apparently mutually exclusive scalar boundary conditions
On a 2D vector Poisson problem with apparently mutually exclusive scalar boundary conditions
This work is devoted to the study of a two-dimensional vector Poisson equation with the normal component of the unknown and the value of the divergence of the unknown prescribed simultaneously on the entire boundary. These two scalar boundary conditions appear prima facie alternative in a standard variational framework. An original variational formulation of this boundary value problem is proposed here. Furthermore, an uncoupled solution algorithm is introduced together with its finite element...
On a class of elliptic systems in .
On a construction of weak solutions to non-stationary Stokes type equations by minimizing variational functionals and their regularity
In this paper, we prove that the regularity property, in the sense of Gehring-Giaquinta-Modica, holds for weak solutions to non-stationary Stokes type equations. For the construction of solutions, Rothe's scheme is adopted by way of introducing variational functionals and of making use of their minimizers. Local estimates are carried out for time-discrete approximate solutions to achieve the higher integrability. These estimates for gradients do not depend on approximation.
On a coupled problem between the plate equation and the membrane equation on polygons
On a free boundary problem for minimal surfaces.
On a model of rotating superfluids
We consider an energy-functional describing rotating superfluids at a rotating velocity , and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical above which energy-minimizers have vortices, evaluations of the minimal energy as a function of , and the derivation of a limiting free-boundary problem.
On a model of rotating superfluids
We consider an energy-functional describing rotating superfluids at a rotating velocity ω, and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical ω above which energy-minimizers have vortices, evaluations of the minimal energy as a function of ω, and the derivation of a limiting free-boundary problem.
On a reaction-diffusion system involving the critical exponent.
In this paper we study the existence and multiplicity of the nontrivial solutions for a given elliptic system with Dirichlet boundary conditions and critical nonlinearity.
On approximation of the Neumann problem by the penalty method
We prove that penalization of constraints occuring in the linear elliptic Neumann problem yields directly the exact solution for an arbitrary set of penalty parameters. In this case there is a continuum of Lagrange's multipliers. The proposed penalty method is applied to calculate the magnetic field in the window of a transformer.
On elliptic systems pertaining to the Schrödinger equation
We discuss the existence of solutions for a system of elliptic equations involving a coupling nonlinearity containing a critical and subcritical Sobolev exponent. We establish the existence of ground state solutions. The concentration of solutions is also established as a parameter λ becomes large.
On minima of variational problems with some nonconvex constraints.
On multiply connected mesoscopic superconducting structures
On nonlinear hemivariational inequalities [Book]
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 quasiconvex equimeasurable rearrangement, a counterexample and an example.
On the concentration of solutions of singularly perturbed Hamiltonian systems in .
On the definition and the lower semicontinuity of certain quasiconvex integrals
On the existence of a component-wise positive radially symmetric solution for a superlinear system.
On the ground states of vector nonlinear Schrödinger equations