TY - JOUR
T1 - Quantitative stability estimates for a two-phase Serrin-type overdetermined problem
AU - Cavallina, Lorenzo
AU - Poggesi, Giorgio
AU - Yachimura, Toshiaki
N1 - Funding Information:
The first author is partially supported by JSPS Grant-in-Aid for Research Activity Start-up Grant Number JP20K22298 . The second author is supported by the Australian Laureate Fellowship FL190100081 “Minimal surfaces, free boundaries and partial differential equations” and is member of AustMS and INdAM/GNAMPA. The third author is partially supported by JSPS Grant-in-Aid for Early-Career Scientists Grant Number JP21K13822 .
Publisher Copyright:
© 2022 Elsevier Ltd
PY - 2022/9
Y1 - 2022/9
N2 - In this paper, we deal with an overdetermined problem of Serrin-type with respect to a two-phase elliptic operator in divergence form with piecewise constant coefficients. In particular, we consider the case where the two-phase overdetermined problem is close to the one-phase setting. First, we show quantitative stability estimates for the two-phase problem via a one-phase stability result. Furthermore, we prove non-existence for the corresponding inner problem by the aforementioned two-phase stability result.
AB - In this paper, we deal with an overdetermined problem of Serrin-type with respect to a two-phase elliptic operator in divergence form with piecewise constant coefficients. In particular, we consider the case where the two-phase overdetermined problem is close to the one-phase setting. First, we show quantitative stability estimates for the two-phase problem via a one-phase stability result. Furthermore, we prove non-existence for the corresponding inner problem by the aforementioned two-phase stability result.
KW - Overdetermined problem
KW - Serrin's problem
KW - Stability
KW - Transmission condition
KW - Two-phase
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U2 - 10.1016/j.na.2022.112919
DO - 10.1016/j.na.2022.112919
M3 - Article
AN - SCOPUS:85129269758
SN - 0362-546X
VL - 222
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
M1 - 112919
ER -