EAN: 9783031132377

REGULARITY OF THE ONE-PHASE FREE BOUNDARIES - B...

This open access book is an introduction to the regularity theory for free boundary problems.
The focus is on the one-phase Bernoulli problem  which is of particular interest as it deeply
influenced the development of the modern free boundary regularity theory and is still an object
of intensive research. The exposition is organized around four main theorems  which are
dedicated to the one-phase functional in its simplest form. Many of the methods and the
techniques presented here are very recent and were developed in the context of different free
boundary problems. We also give the detailed proofs of several classical results  which are
based on some universal ideas and are recurrent in the free boundary  PDE and the geometric
regularity theories. This book is aimed at graduate students and researches and is accessible
to anyone with a moderate level of knowledge of elliptical PDEs.

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