On a Local Existence Theorem of Neumann Problem for Some Quasilinear Hyperbolic Systems of 2nd Order.
On a magnetic characterization of spectral minimal partitions
Given a bounded open set in (or in a Riemannian manifold) and a partition of by open sets , we consider the quantity where is the ground state energy of the Dirichlet realization of the Laplacian in . If we denote by the infimum over all the -partitions of , a minimal -partition is then a partition which realizes the infimum. When , we find the two nodal domains of a second eigenfunction, but the analysis of higher ’s is non trivial and quite interesting. In this paper, we give...
On a mathematical model for the crystallization of polymers
We consider a mathematical model proposed in [1] for the cristallization of polymers, describing the evolution of temperature, crystalline volume fraction, number and average size of crystals. The model includes a constraint on the crystal volume fraction. Essentially, the model is a system of both second order and first order evolutionary partial differential equations with nonlinear terms which are Lipschitz continuous, as in [1], or Hölder continuous, as in [3]. The main novelty here is the...
On a maximum principle for elliptic systems with constant coefficients
On a maximum principle for weak solutions of the stationary Stokes system
On a method for solving a classical variational problem.
On a Method of K. Uhlenbeck for Proving Partial Regularity for Solutions of Certain Nonlinear Elliptic Systems.
On a mixed boundary values problem for Lavrentev type equations
On a mixed problem for a linear coupled system with variable coefficients.
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 Navier-Stokes type equation and inequality
A Navier-Stokes type equation corresponding to a non-linear relationship between the stress tensor and the velocity deformation tensor is studied and existence and uniqueness theorems for the solution, in the 3-dimensional case, of the Cauchy-Dirichlet problem, for a bounded solution and for an almost periodic solution are given. An inequality which in some sense is the limit of the equation is also considered and existence theorems for the solution of the Cauchy-Dirichlet problems and for a periodic...
On a necessary and sufficient condition for a blowing up of a solution to a mixed boundary problem for a certain nonlinear equation of Sobolev type.
On a nonlinear coupled system with internal damping.
On a nonlinear eigenvalue problem in Sobolev spaces with variable exponent.
On a nonlinear elliptic system: resonance and bifurcation cases
In this paper we consider an elliptic system at resonance and bifurcation type with zero Dirichlet condition. We use a Lyapunov-Schmidt approach and we will give applications to Biharmonic Equations.
On a nonlinear wave equation with damping.
On a nonlocal eigenvalue problem
On a nonresonance condition between the first and the second eigenvalues for the -Laplacian.
On a nonstationary model of a catalytic process in a fluidized bed.