| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Estadual Campinas, IMECC, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil
[2] Royal Inst Technol, Dept Math, S-10044 Stockholm - Sweden
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | INTERFACES AND FREE BOUNDARIES; v. 19, n. 3, p. 351-369, 2017. |
| Web of Science Citations: | 0 |
| Abstract | |
We study a minimum problem for a non-differentiable functional whose reaction term does not have scaling properties. Specifically we consider the functional (sic)(v) = integral(Omega) (vertical bar del v vertical bar(2)/2 - v(+)(log v - 1))dx -> min which should be minimized in some natural admissible class of non-negative functions. Here, v(+) = max[0, v]. The Euler-Lagrange equation associated with (sic) is -Delta u = chi([u>0]) log u, which becomes singular along the free boundary partial derivative[u > O]. Therefore, the regularity results do not follow from classical methods. Besides, the logarithmic forcing term does not have scaling properties, which are very important in the study of free boundary theory. Despite these difficulties, we obtain optimal regularity of a minimizer and show that, close to every free boundary point, they exhibit a super-characteristic growth like r(2)vertical bar log r vertical bar. This estimate is crucial in the study of analytic and geometric properties of the free boundary. (AU) | |
| FAPESP's process: | 12/20197-0 - Local aspects of eliptic and parabolic problems |
| Grantee: | Olivâine Santana de Queiroz |
| Support Opportunities: | Regular Research Grants |