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http://hdl.handle.net/2445/194026
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DC Field | Value | Language |
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dc.contributor.author | Fernandez-Real, Xavier | - |
dc.contributor.author | Ros, Xavier | - |
dc.date.accessioned | 2023-02-23T13:35:09Z | - |
dc.date.available | 2023-02-23T13:35:09Z | - |
dc.date.issued | 2019-09 | - |
dc.identifier.issn | 1078-0947 | - |
dc.identifier.uri | http://hdl.handle.net/2445/194026 | - |
dc.description.abstract | Motivated by its relation to models of flame propagation, we study globally Lipschitz solutions of $\Delta u=f(u)$ in $\mathbb{R}^n$, where $f$ is smooth, nonnegative, with support in the interval $[0,1]$. In such setting, any 'blow-down' of the solution $u$ will converge to a global solution to the classical onephase free boundary problem of Alt-Caffarelli. In analogy to a famous theorem of Savin for the Allen-Cahn equation, we study here the $1 \mathrm{D}$ symmetry of solutions $u$ that are energy minimizers. Our main result establishes that, in dimensions $n<6$, if $u$ is axially symmetric and stable then it is $1 \mathrm{D}$. | - |
dc.format.extent | 15 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | American Institute of Mathematical Sciences (AIMS) | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.3934/dcds.2019238 | - |
dc.relation.ispartof | Discrete and Continuous Dynamical Systems-Series A, 2019, vol. 39, num. 12, p. 6945-6959 | - |
dc.relation.uri | https://doi.org/10.3934/dcds.2019238 | - |
dc.rights | (c) American Institute of Mathematical Sciences (AIMS), 2019 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Laplacià | - |
dc.subject.classification | Equacions diferencials el·líptiques | - |
dc.subject.classification | Equacions en derivades parcials | - |
dc.subject.classification | Distribució (Teoria de la probabilitat) | - |
dc.subject.other | Laplacian operator | - |
dc.subject.other | Elliptic differential equations | - |
dc.subject.other | Partial differential equations | - |
dc.subject.other | Distribution (Probability theory) | - |
dc.title | On global solutions to semilinear elliptic equations related to the one-phase free boundary problem | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 708570 | - |
dc.date.updated | 2023-02-23T13:35:09Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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708570.pdf | 396.44 kB | Adobe PDF | View/Open |
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