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01254nam a2200181Ia 4500 |
| 001 |
10.1016-j.aim.2022.108380 |
| 008 |
220425s2022 CNT 000 0 und d |
| 020 |
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|a 00018708 (ISSN)
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| 245 |
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|a Interface regularity for semilinear one-phase problems
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| 260 |
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|b Academic Press Inc.
|c 2022
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| 856 |
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|z View Fulltext in Publisher
|u https://doi.org/10.1016/j.aim.2022.108380
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|a 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 C1,α 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 RN, for N≤4, answering positively a conjecture of Fernández-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. © 2022 The Author(s)
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|a Blow-down
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|a Improvement of flatness
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|a One-phase free boundary problem
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| 700 |
1 |
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|a Audrito, A.
|e author
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|a Serra, J.
|e author
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| 773 |
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|t Advances in Mathematics
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