Journal
ADVANCES IN MATHEMATICS
Volume 403, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2022.108380
Keywords
Blow-down; Improvement of flatness; One-phase free boundary problem
Categories
Funding
- European Union [892017]
- European Research Council (ERC) [948029]
- European Research Council (ERC) [948029] Funding Source: European Research Council (ERC)
- Marie Curie Actions (MSCA) [892017] Funding Source: Marie Curie Actions (MSCA)
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We study critical points of a one-parameter family of functionals arising in combustion models. The problems we consider converge, for infinitesimal values of the parameter, to Bernoulli's free boundary problem. We prove C-1, C-alpha estimates for the interfaces and obtain the one-dimensional symmetry of minimizers. Our results are analogous to Savin's results for the Allen-Cahn equation in the context of Bernoulli's free boundary problem.
We study critical points of a one-parameter family of functionals arising in combustion models. The problems we consider converge, for infinitesimal values of the parameter, to Bernoulli's free boundary problem, also known as one phase problem. We prove a C-1,C-alpha estimates for the interfaces (level sets separating the burnt and unburnt regions). As a byproduct, we obtain the one-dimensional symmetry of minimizers in the whole R-N, for N <= 4, answering positively a conjecture of Fernandez-Real and Ros-Oton. Our results are to Bernoulli's free boundary problem what Savin's results for the Allen-Cahn equation are to minimal surfaces. (c) 2022 The Author(s). Published by Elsevier Inc.
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