Regularity of free boundaries a heuristic retro.
This survey concerns regularity theory of a few free boundary problems that have been developed in the past half a century. Our intention is to bring up different ideas and techniques that constitute the fundamentals of the theory. We shall discuss four different problems, where approaches are somewhat different in each case. Nevertheless, these problems can be divided into two groups: (i) obstacle and thin obstacle problem; (ii) minimal surfaces, and cavitation flow of a perfect fluid. In each case, we shall only discuss the methodology and approaches, giving basic ideas and tools that have been specifically designed and tailored for that particular problem. The survey is kept at a heuristic level with mainly geometric interpretation of the techniques and situations in hand.
Department of Mathematics, The University of Texas at Austin, Austin, TX 78712-1202, USA.
Luis A
LA
Caffarelli
Department of Mathematics, KTH Royal Institute of Technology, Stockholm 100 44, Sweden henriksh@kth.se.
Henrik
H
Shahgholian
cavitation; minimal surfaces; obstacle; regularity for free boundaries; thin obstacle