Boundary value problems with a free boundary in the theory of stationary filtration

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From the text: "The problem of steady-state filtration in porous media leads to a boundary value problem with a free boundary for  a linear differential equation of elliptic type. C. Baiocchi [Ann. Mat. Pura Appl. (4) 92 (1972), 107–127; MR0408443] proposed a new technique for solving such problems. Not only does this technique permit one to obtain theoretical results which are rigorous from the mathematical point of view, but it is also useful in applications. The main idea consists in reducing the boundary value problem to a certain variational inequality. This technique was first applied to the solution of a basic model problem, but subsequently its applications were broadened and it was applied to more general cases.  In this essay we offer the reader a compact presentation of the fundamental results derived in this area during the last few years."