TY - JOUR
T1 - Higher regularity of the free boundary in a semilinear system
AU - Fotouhi, Morteza
AU - Koch, Herbert
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023.
PY - 2024/4
Y1 - 2024/4
N2 - In this paper we are concerned with higher regularity properties of the elliptic system (Formula presented.) for 0≤q<1. We show analyticity of the regular part of the free boundary ∂{|u|>0}, analyticity of |u|1-q2 and u|u| up to the regular part of the free boundary. Applying a variant of the partial hodograph-Legendre transformation and the implicit function theorem, we arrive at a degenerate equation, which introduces substantial challenges to be dealt with. Along the lines of our study, we also establish a Cauchy-Kowalevski type statement to show the local existence of solution when the free boundary and the restriction of u|u| from both sides to the free boundary are given as analytic data.
AB - In this paper we are concerned with higher regularity properties of the elliptic system (Formula presented.) for 0≤q<1. We show analyticity of the regular part of the free boundary ∂{|u|>0}, analyticity of |u|1-q2 and u|u| up to the regular part of the free boundary. Applying a variant of the partial hodograph-Legendre transformation and the implicit function theorem, we arrive at a degenerate equation, which introduces substantial challenges to be dealt with. Along the lines of our study, we also establish a Cauchy-Kowalevski type statement to show the local existence of solution when the free boundary and the restriction of u|u| from both sides to the free boundary are given as analytic data.
UR - https://www.scopus.com/pages/publications/85153937321
U2 - 10.1007/s00208-023-02620-y
DO - 10.1007/s00208-023-02620-y
M3 - Article
AN - SCOPUS:85153937321
SN - 0025-5831
VL - 388
SP - 3897
EP - 3939
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 4
ER -