Su un problema di frontiera libera connesso a questioni di idraulica

An up-wind finite element method for a filtration problem

“…We choose as " exact solution " the solution of the same problem computed via Baiocchi's transform (see [4]) with a mesh size h = 1/60. The transformation leads to the resolution of a variational inequality in the new unknown w, with -w y = u.…”

“…( 1 2) For a theoretical study of problem (1 2) In case of more restrictive assumptions on the geometry of the domain Q, other formulations of the problem are known : see, for instance, Baiocchi [4] (transformation of the problem in a vanational mequahty), Baiocchi [5] (transformation in a quasi-vanational mequahty) and Baiocchi-Capelo [6] (for complete références about these probiems). These formulations are the starting point for a numerical study of the problem, see for instance [7] and [6] (for the further références)…”

“…A great improvement to the theory was introduced by Baiocchi (see e.g. [4]), who formulated the problem, in the special case of a rectangular domain, on a rigorous mathematical basis, transforming it into a variational inequality of obstacle type. This idea was then generalized (see e.g.…”

A free boundary value problem in potential theory

“…We shall solve Problem 1 by means of a variational inequality suggested by the properties of a function g(z) which satisfies (1)(2)(3)(4)(5) gp = -p-T he idea of introducing a new unknown related to the original one through differentiation is due to C. Baiocchi [1] who studied a filtration problem. It has subsequently been employed by H. Brezis and G. Stampacchia [5], V. Benci [2], Duvaut [6], and also in [12].…”

A direct algorithm in some free boundary problems

“…Free boundary problems are described by nonlinear partial differential equations modelling important applications from physics like change of phase phenomena, contact problems in elasticity, flow propagation in porous media, etc, [3,9].…”