Titlebook: Regularity of the One-phase Free Boundaries; Bozhidar Velichkov Book‘‘‘‘‘‘‘‘ 2023 The Editor(s) (if applicable) and The Author(s) 2023 Ope

Inflammation

Non-degeneracy of the Local Minimizers,In this section we prove the non-degeneracy of the solutions to the one-phase problem (.). Our main result is the following.

混雜人

Measure and Dimension of the Free Boundary,This chapter is dedicated to the measure theoretic structure of the free boundary . Ω.. The results presented here are mainly a consequence of the Lipschitz continuity and the non-degeneracy of the minimizer . (Theorem . and Proposition .).

改正

結(jié)合

豎琴

The Weiss Monotonicity Formula and Its Consequences,This chapter is dedicated to the monotonicity formula for the boundary adjusted energy introduced by Weiss in [.]. Precisely, for every Λ?≥?0 and every .?∈?..(..).

殺死

Dimension of the Singular Set,In this chapter, we prove Theorem .. As in the original work of Weiss (see [.]), we will use the so-called Federer’s dimension reduction principle, which first appeared in [.].

性上癮

Ergots

An Epiperimetric Inequality Approach to the Regularity of the One-Phase Free Boundaries,Throughout this section, we will use the notation . where .. is the unit ball in ., .?≥?2 and .?∈?..(..).

使迷惑

小丑

978-3-031-13237-7The Editor(s) (if applicable) and The Author(s) 2023