On a problem of the theory of lubrication governed by a variational inequality

The hydrodynamic lubrication of a complete journal bearing of finite width is studied using the theory of variational inequalities: we deal mainly with existence, uniqueness and regularity of the solution.     

A free boundary problem in the theory of electrically actuated microdevices

Electrostatically deflected elastic systems are increasingly used in technical applications. We study a typical situation as a free boundary problem and prove, under quite general hypotheses, the existence of a local branch of solutions. Hadamard’s variational formula is crucial in the proof, which is based on the implicit function theorem in Banach spaces.     

Existence of weak solutions for the nonstationary problem of the Joule heating of a conductor

Summary An initial-boundary value problem for a system of two nonlinear partial differential equations is studied using the Faedo-Galerkin method. The problem describes the electric heating of a conducting body. The main result is a theorem of existence of weak solutions for an arbitrarily large interval of time.     

Invariant regions for the Nernst-Planck equations

We consider a coupling between the Nernst-Planck equations and the Navier-Stokes system; we study the stationary and the evolution problems. The crucial property turns out to be the existence of an invariant region. An asymptotic result in the case of Neumann boundary conditions is also given.     

An hyperbolic system of P.D.E. relevant in general relativity

Ricerche di Matematica - Assuming as starting point the validity of the Einstein-Rosen metric we study the hyperbolic system of P.D.E. to which the Einstein’s field equations can be reduced....     

The plane stress problem of Ghizzetti in elasto-plasticity

The theory of variational inequalities is applied to some special problems of elastic-plastic deformation.     

On certain nonlinear problems arising in the theory of lubrication

Various nonlinear elliptic boundary value problems motivated by the theory of lubrication are stated and studied. We deal mainly with the aspects of existence and uniqueness of solutions.     

Existence results for a nonlinear elliptic system modelling a temperature dependent electrical resistor

Summary The electrical resistance in many substances varies greatly with the temperature which in turns depends on the Joule effect. This nonlinear effect is described under steady conditions by a system of nonlinear elliptic equations with a quadratic growth in the gradient. This work gives a theorem of existence for the related elliptic boundary value problem.     

A note on existence, uniqueness and continuous dependence for a non-linear heat conduction problem

^** Email: cimatti{at}dm.unipi.it Using the Levy–Caccioppoli global inversion theorem, aresult of existence, uniqueness and continuous dependence isproved for a non-linear problem of heat conduction.