The goal of the paper (minicourse) is the study of the two-phase steady- state Stefan problem and some related conduction problems with or without phase change through the theory of elliptic variational inequalities. The material is organized in four Chapters and three Appendices. In the introductory Chapter generalities on elliptic variational inequalities (EVI) with a symmetric bilinear form and variational formulations for elliptic boundary value problems in Sobolev spaces are given. In Chapters II and III the EVI theory is applied to the two steady-state two-phase Stefan problems and related conduction problems in a bounded domain $Ω\subset{\bbfR}\sp n$. In Chapter IV entitled: “An evolution two-phase Stefan problem for a semi-infinite material” conditions for several heat fluxes on the fixed face are given to obtain an instantaneous evolution two-phase Stefan problem for a semi-infinite material with constant initial temperature. In Appendix 1 three examples are given with explicit solutions to related problems presented in Chapters II and III. The last two Appendices present short reviews on the numerical approximations for BVP of Stefan type.
Reviewer: G.Aniculaesei (Iaşi)